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All questions of Motion in a Plane for JEE Exam
If 
what is the angle between 
and 
- a)900
- b)300
- c)600
- d)450
Correct answer is option 'D'. Can you explain this answer?
If what is the angle between and
what is the angle between and a)
900
b)
300
c)
600
d)
450
|
Gaurav Kumar answered |
We know that for two vectors P and Q
P.Q = |P||Q| cos a
And PxQ = |P||Q| sin a
Where a is angle between them
When P.Q = PxQ
We get sin a = cos a
Thus a = 450
P.Q = |P||Q| cos a
And PxQ = |P||Q| sin a
Where a is angle between them
When P.Q = PxQ
We get sin a = cos a
Thus a = 450
A car travelling at 36km/h-1 due North turns West in 5 seconds and maintains the same speed. What is the acceleration of the car?
- a)2√2ms-2 South West
- b)√2ms-2 South West
- c)2ms-2 North West
- d)4ms-2 North West
Correct answer is option 'A'. Can you explain this answer?
A car travelling at 36km/h-1 due North turns West in 5 seconds and maintains the same speed. What is the acceleration of the car?
a)
2√2ms-2 South West
b)
√2ms-2 South West
c)
2ms-2 North West
d)
4ms-2 North West
|
Rahul Bansal answered |
Initial velocity of car = 36 km/hr due north
Final velocity of car = 36 km/hr due west
magnitude of change in velocity = root[(36)^2 + (36)^2] = 36 x √2
(since velocity is a vector, so direction has to be taken into account)
Acceleration = Change in velocity/time = [36√2 x 5/18]/5 m/s^2 = 2√2 m/s^2 = 2.828 m/s^2
A particle has an initial velocity 3 iˆ +4 jˆ and an acceleration 0.4 iˆ + 0.3 jˆ .Its speed after 10 s is- a)7 units
- b)8.5 units
- c)7√2 units
- d)10 units
Correct answer is 'B'. Can you explain this answer?
A particle has an initial velocity 3 iˆ +4 jˆ and an acceleration 0.4 iˆ + 0.3 jˆ .Its speed after 10 s is
a)
7 units
b)
8.5 units
c)
7√2 units
d)
10 units
|
Mira Sharma answered |
Answer is C) 7 x (2)^1/2
Solution:
The initial velocity is given by
u = v - at
Where, v = Final Velocity, t = time taken, and a = acceleration
u = 3 i + 4 j
a = 0.4 i + 0.3 j
t = 10 s
Using initial velocity formula
3 i + 4 j = v - (0.4 i + 0.3 j) 10
v = 7 ( i + j)
Velocity is the vector quantity which is defined by both magnitude and direction but speed is scalar quantity which is defined by only magnitude.
The magnitude of v = (7^2+7^2)^1/2 = 7 x (2)^1/2
A boat sails across a river with a velocity of 10 km/hr. If resultant boat velocity is 14 km/hr, then what is the velocity of river water?
- a) 17.20 km/hr
- b) 10 km/hr
- c) 9.79 km/hr
- d) 4.88 km/hr
Correct answer is option 'C'. Can you explain this answer?
A boat sails across a river with a velocity of 10 km/hr. If resultant boat velocity is 14 km/hr, then what is the velocity of river water?
a)
17.20 km/hr
b)
10 km/hr
c)
9.79 km/hr
d)
4.88 km/hr
|
Om Desai answered |
We can use the Pythagorean theorem to solve this problem since the boat's velocity, river's velocity, and resultant velocity form a right triangle.
Let the boat's velocity be represented by A (10 km/hr), the river's velocity be represented by B, and the resultant velocity be represented by C (14 km/hr).
According to the Pythagorean theorem, A^2 + B^2 = C^2.
Now, we can plug in the given values and solve for B:
(10)^2 + B^2 = (14)^2
100 + B^2 = 196
Subtract 100 from both sides:
B^2 = 96
Now, take the square root of both sides:
B = sqrt(96) ≈ 9.79 km/hr
Let the boat's velocity be represented by A (10 km/hr), the river's velocity be represented by B, and the resultant velocity be represented by C (14 km/hr).
According to the Pythagorean theorem, A^2 + B^2 = C^2.
Now, we can plug in the given values and solve for B:
(10)^2 + B^2 = (14)^2
100 + B^2 = 196
Subtract 100 from both sides:
B^2 = 96
Now, take the square root of both sides:
B = sqrt(96) ≈ 9.79 km/hr
A particle moves in x-y plane starting from the origin in a direction making 30° angle with x-axis. Distance covered by it is 5 m. what is the position vector of the particle.- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
A particle moves in x-y plane starting from the origin in a direction making 30° angle with x-axis. Distance covered by it is 5 m. what is the position vector of the particle.
a)
b)
c)
d)
|
Ankita Menon answered |
Initial velocity = u = 20 m/s
Final velocity = v = 0 [ at maximum height , v = 0 ]
Final velocity = v = 0 [ at maximum height , v = 0 ]
Acceleration due to gravity(g) in this case , is taken as negative.
This is because , when the direction of motion of object is opposite to "g" , then value of g is taken as -ve
This is because , when the direction of motion of object is opposite to "g" , then value of g is taken as -ve
hence ,
g = -9.8 m/s²
Let's use the formula :-
[h = height ]
v² -u² = 2gh
0² - 20² = 2*-9.8*h
-400 = -19.6h
h = -400/-19.6
= 20.408 m [ approximately ]
-400 = -19.6h
h = -400/-19.6
= 20.408 m [ approximately ]
How many directions are possible for the same horizontal range?- a)4
- b)3
- c)2
- d)1
Correct answer is option 'C'. Can you explain this answer?
How many directions are possible for the same horizontal range?
a)
4
b)
3
c)
2
d)
1
|
Mira Joshi answered |
We know that the horizontal range for any projectile motion let say R = 2u2.sin 2a /g
Where u is initial speed, and a is the angle at which the particle is thrown, which is responsible for direction. So in between the possible range of a that is 0 - 90, there are maximum two equal values of sin 2a, thus the maximum number of directions for the same or equal range are 2.
Where u is initial speed, and a is the angle at which the particle is thrown, which is responsible for direction. So in between the possible range of a that is 0 - 90, there are maximum two equal values of sin 2a, thus the maximum number of directions for the same or equal range are 2.
Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella?- a)cos-1 1/3
- b)sin-1 1/3
- c)tan-1 2/3
- d)tan-1 1/3
Correct answer is option 'D'. Can you explain this answer?
Rain is falling vertically with the speed of 30 m/s. A man rides a bicycle with the speed of 10 m/s in east to west direction. What is the direction in which he should hold the umbrella?
a)
cos-1 1/3
b)
sin-1 1/3
c)
tan-1 2/3
d)
tan-1 1/3
|
Krishna Iyer answered |
When the man rides, he should put an umbrella in the opposite direction to which the drops are falling with respect to him.
Hence wrt man, the speed of rain drop is
at an angle of tan-1 ⅓
Hence he would put umbrella to the direction of tan-1 ⅓
Hence wrt man, the speed of rain drop is
at an angle of tan-1 ⅓Hence he would put umbrella to the direction of tan-1 ⅓
A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top- a)1 s
- b)2 s
- c)4 s
- d)16 s
Correct answer is option 'B'. Can you explain this answer?
A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top
a)
1 s
b)
2 s
c)
4 s
d)
16 s
|
Naina Sharma answered |
A body start from rest so, u = 0
Let total distance covered = s
Let a body moves with accerlation = a
► s = 1/2 × a× t2
► s = 1/2× a × 42
► s = 8a
The one-fourth of total distance, s' = 8a/4
= 2a
► s' = 1/2 × a × t2
► 2a / a = 1/2 × t2
► 4 = t2
► t = 2 s
Let total distance covered = s
Let a body moves with accerlation = a
► s = 1/2 × a× t2
► s = 1/2× a × 42
► s = 8a
The one-fourth of total distance, s' = 8a/4
= 2a
► s' = 1/2 × a × t2
► 2a / a = 1/2 × t2
► 4 = t2
► t = 2 s
A battle ship simultaneously fires two shells at enemy ships. Both are fired with the same speed but with different directions as shown. If the shells follow the parabolic trajectories shown, which ship gets hit first?
- a)they get hit at the same time.
- b)ship μ2
- c)need more information about the trajectories.
- d)ship μ1
Correct answer is 'B'. Can you explain this answer?
A battle ship simultaneously fires two shells at enemy ships. Both are fired with the same speed but with different directions as shown. If the shells follow the parabolic trajectories shown, which ship gets hit first?
a)
they get hit at the same time.
b)
ship μ2
c)
need more information about the trajectories.
d)
ship μ1
|
|
Krishna Iyer answered |
Ship 2 gets hit first. The time of flight only depends on the y-component of motion, not the x-component. The higher you throw something up in the air, the more time it spends in the air. It can also be shown from equation-
y=v0y t – ½ g t2=0
v0y for projectile μ1 is greater than for μ2.
Which statement is true for a ball thrown at 20 degrees with the horizontal, when it is at the highest point in its trajectory?- a)Its velocity is zero but its acceleration is nonzero
- b)Its velocity is nonzero but its acceleration is zero
- c)Its velocity and acceleration are both zero
- d)Its velocity is perpendicular to its acceleration
Correct answer is option 'D'. Can you explain this answer?
Which statement is true for a ball thrown at 20 degrees with the horizontal, when it is at the highest point in its trajectory?
a)
Its velocity is zero but its acceleration is nonzero
b)
Its velocity is nonzero but its acceleration is zero
c)
Its velocity and acceleration are both zero
d)
Its velocity is perpendicular to its acceleration
|
Suresh Reddy answered |
At the highest point in its trajectory, the acceleration (g) is acting in downward direction, whereas velocity of the projectile is only in the X (horizontal) direction.
The quantity which remains unchanged during the flight of an oblique projectile is- a)Horizontal component of acceleration
- b)Vertical component of acceleration
- c)Vertical component of velocity
- d)Horizontal component of velocity
Correct answer is option 'D'. Can you explain this answer?
The quantity which remains unchanged during the flight of an oblique projectile is
a)
Horizontal component of acceleration
b)
Vertical component of acceleration
c)
Vertical component of velocity
d)
Horizontal component of velocity
|
Sarthak Rajendra Bande answered |
As there is no horizontal acceleration is present in oblique projection horizontal component of velocity is constant
If an object is dropped through the window of a fast running train. Then- a)the object moves straight horizontally.
- b)to a man standing near the track, path of the object will be a part of parabola.
- c)the object falls down vertically.
- d)the object will follow an elliptical path
Correct answer is option 'B'. Can you explain this answer?
If an object is dropped through the window of a fast running train. Then
a)
the object moves straight horizontally.
b)
to a man standing near the track, path of the object will be a part of parabola.
c)
the object falls down vertically.
d)
the object will follow an elliptical path
|
|
Suresh Reddy answered |
When an object is still held it is the part of a system in which the train is moving, once it is left it still has the same velocity as the train for a person from ground. Thus as the velocity is horizontal and acceleration is vertical, it would follow a parabolic trajectory.
A body is thrown with a velocity of 10m/s at an angle of 60 degrees with the horizontal. Its velocity at the highest point is: - a)5 m/s
- b)8.7 m/s
- c)10 mis
- d)0
Correct answer is option 'A'. Can you explain this answer?
A body is thrown with a velocity of 10m/s at an angle of 60 degrees with the horizontal. Its velocity at the highest point is:
a)
5 m/s
b)
8.7 m/s
c)
10 mis
d)
0
|
|
Mira Joshi answered |
At the highest point, its vertical velocity will become zero. Hence the only left velocity is horizontal which remains unchanged and is equal to 10 cos 60 = 5m/s
Vectors can be added by- a)adding the magnitudes of the vectors
- b)adding the angles of the vectors
- c)translating the two vectors
- d)parallelogram law of addition
Correct answer is option 'D'. Can you explain this answer?
Vectors can be added by
a)
adding the magnitudes of the vectors
b)
adding the angles of the vectors
c)
translating the two vectors
d)
parallelogram law of addition
|
Puja Kaur answered |
Explanation:Parallelogram law of vector addition is,If two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a diagonal passing through the point of contact of two vectors.
The vector which when added to the resultant of 
and 
gives unit vector along x direction.- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
The vector which when added to the resultant of and gives unit vector along x direction.
and gives unit vector along x direction.a)
b)
c)
d)
|
Naveen Choudhary answered |
Time taken by first drop to cover 5 cm, u = 0
⇒ h = 1/2 gt2
⇒ 5 = 1/2 x 10 x t2
⇒ t = 1 sec
Hence interval is 0.5 sec for each drop.
Now distance fallen by second drop in 0.5 sec
⇒ h1 = 1/2 gt2
= 1/2 x 10 x (0.5)2
= 5 x 0.25
= 1.25 m
Height above the ground ( of 2nd drop) = 5 - 1.25
= 3.75 m
The angular speed of a wheel of radius 0.50 m moving with the speed of 20 m/s is:- a)40 radian/s
- b)10 radian/s
- c)30 radian/s
- d)20 radian/s
Correct answer is option 'A'. Can you explain this answer?
The angular speed of a wheel of radius 0.50 m moving with the speed of 20 m/s is:
a)
40 radian/s
b)
10 radian/s
c)
30 radian/s
d)
20 radian/s
|
Pooja Mehta answered |
Radius r = 0.5 m
Speed, v = 20 m/s
We know,
v = r ω
where,
ω = angular velocity
20 = 0.5 x ω
ω = 20/0.5 = 40 rad/sec
A monkey is running on the ground, next to a train, in the direction of the train. The speed of the monkey is 5km/h and the speed of the train is 100km/h. What is the velocity of the monkey with respect to the train?- a)105km/h in the direction opposite to the train
- b)95 km/h in the direction of the train
- c)105km/h in the direction of the train
- d)95 km/h in the direction opposite to the train.
Correct answer is option 'D'. Can you explain this answer?
A monkey is running on the ground, next to a train, in the direction of the train. The speed of the monkey is 5km/h and the speed of the train is 100km/h. What is the velocity of the monkey with respect to the train?
a)
105km/h in the direction opposite to the train
b)
95 km/h in the direction of the train
c)
105km/h in the direction of the train
d)
95 km/h in the direction opposite to the train.
|
|
Riya Banerjee answered |
Assuming the direction of velocity of train to be positive, wrt train the speed of monkey will be
-100 + 5 = -95 kmph
I.. 95 kmph in direction opposite to the train.
-100 + 5 = -95 kmph
I.. 95 kmph in direction opposite to the train.
In 5 seconds a body covers a distance of 50 m and in 10 seconds it covers 80 m with uniform acceleration. What is the distance traveled in 15 seconds?
- a) 100 m
- b) 110 m
- c) 1000 m
- d) None of the above
Correct answer is option 'D'. Can you explain this answer?
In 5 seconds a body covers a distance of 50 m and in 10 seconds it covers 80 m with uniform acceleration. What is the distance traveled in 15 seconds?
a)
100 m
b)
110 m
c)
1000 m
d)
None of the above
|
Anjana Sharma answered |
ω = 2πT
where
T = Time period of revolution of earth around its own axis
= 24 hours
=24 x 60 x 60
=86400 s
Hence,
ω = 2π/86400
= π/43200 rad s^-1
When a projectile is thrown up at an angle θ to the ground, the time taken by it to rise and to fall are related as- a)time of rise can be less than or equal to time of fall
- b)they are equal
- c)time of rise < time of fall
- d)time of rise > time of fall
Correct answer is option 'B'. Can you explain this answer?
When a projectile is thrown up at an angle θ to the ground, the time taken by it to rise and to fall are related as
a)
time of rise can be less than or equal to time of fall
b)
they are equal
c)
time of rise < time of fall
d)
time of rise > time of fall
|
|
Gaurav Kumar answered |
The time of fall or rise for a projectile depends upon its vertical component of initial velocity and the vertical acceleration. As the acceleration does not change and the motion of path is identical for the rise phase and the fall phase, we can easily deduce that time taken is also the same.
At the point of maximum height, the acceleration is:- a)minimum
- b)g
- c)maximum
- d)zero
Correct answer is option 'B'. Can you explain this answer?
At the point of maximum height, the acceleration is:
a)
minimum
b)
g
c)
maximum
d)
zero
|
|
Suresh Iyer answered |
At a point of maximum height, the derivative of displacement i.e. velocity is zero but as the gravitational acceleration is equal at all near points to the surface of earth, acceleration at maximum height is still equal to g.
A ship A sailing due east with a velocity of 10 km/h happens to appear sailing due north with a velocity of 5 km/h, to a person, sitting in a moving ship B. Determine the velocity (absolute) of ship B.
.
- a)
5√5 km/h, tan−1(1/2) S of E
- b)5√5 km/h, tan−1(1/2) E of S
- c)4√5 km/h, tan−1(1/2) S of E
- d)4√5 km/h, tan−1(1/2) E of S
Correct answer is option 'A'. Can you explain this answer?
A ship A sailing due east with a velocity of 10 km/h happens to appear sailing due north with a velocity of 5 km/h, to a person, sitting in a moving ship B. Determine the velocity (absolute) of ship B.
.
a)
5√5 km/h, tan−1(1/2) S of E
b)
5√5 km/h, tan−1(1/2) E of S
c)
4√5 km/h, tan−1(1/2) S of E
d)
4√5 km/h, tan−1(1/2) E of S
|
Preeti Iyer answered |
Here we are given velocity of 'A', 
Velocity of 'A', w.r.t. 'B',
Velocity of 'A', w.r.t. 'B',
Now,
Hence velocity of B, 
Hence velocity of B, i.e.
S of E
S of EThe angular speed of a wheel of radius 0.50 m moving with the speed of 20 m/s is:- a)40 radian/s
- b)30 radins/s
- c)20 radians/s
- d)10 radians/s
Correct answer is option 'A'. Can you explain this answer?
The angular speed of a wheel of radius 0.50 m moving with the speed of 20 m/s is:
a)
40 radian/s
b)
30 radins/s
c)
20 radians/s
d)
10 radians/s
|
|
Rahul Bansal answered |
Radius r = 0.5 m
Speed, v = 20 m/s
We know,
v = r ω
where,
ω = angular velocity
20 = 0.5 x ω
ω = 20/0.5 = 40 rad/sec
A ball is rolled off the edge of a horizontal table at a speed of 4 m/second. It hits the ground after 0.4 second. Which statement given below is true.- a)It hits the ground at a horizontal distance 1.6 m from the edge of the table.
- b)The speed with which it hits the ground is 4.0 m/second.
- c)Height of the table is 0.8 m.
- d)It hits the ground at an angle of 60o to the horizontal.
Correct answer is option 'A,C'. Can you explain this answer?
A ball is rolled off the edge of a horizontal table at a speed of 4 m/second. It hits the ground after 0.4 second. Which statement given below is true.
a)
It hits the ground at a horizontal distance 1.6 m from the edge of the table.
b)
The speed with which it hits the ground is 4.0 m/second.
c)
Height of the table is 0.8 m.
d)
It hits the ground at an angle of 60o to the horizontal.
|
Tejas Verma answered |
Vertical component of velocity of ball at point P
Horizontal component of velocity = initial velocity 
So the speed with which it hits the ground,
and
⇒ θ = 45º
It means the ball hits the ground at an angle of 45∘ to the horizontal.
Height of the table
Height of the table
Horizontal distance travelled by the ball from the edge of table, h = ut = 4 × 0.4 = 1.6 m
The angular speed of the second hand of a watch is :- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
The angular speed of the second hand of a watch is :
a)
b)
c)
d)
|
|
Riya Banerjee answered |
The second hand goes through 2π radians in 1 min, or 2π radian/60 seconds, so ω = π/30 rad.s-1 = 0.03 rad.s-1
A particle has an initial velocity 3 iˆ +4 jˆ and an acceleration 0.4 iˆ + 0.3 jˆ .Its speed after 10 s is- a)7 units
- b)8.5 units
- c)7√2 units
- d)10 units
Correct answer is option 'B'. Can you explain this answer?
A particle has an initial velocity 3 iˆ +4 jˆ and an acceleration 0.4 iˆ + 0.3 jˆ .Its speed after 10 s is
a)
7 units
b)
8.5 units
c)
7√2 units
d)
10 units
|
|
Nandini Patel answered |
Answer is C) 7 x (2)^1/2
Solution:
The initial velocity is given by
u = v - at
Where, v = Final Velocity, t = time taken, and a = acceleration
u = 3 i + 4 j
a = 0.4 i + 0.3 j
t = 10 s
Using initial velocity formula
3 i + 4 j = v - (0.4 i + 0.3 j) 10
v = 7 ( i + j)
Velocity is the vector quantity which is defined by both magnitude and direction but speed is scalar quantity which is defined by only magnitude.
The magnitude of v = (7^2+7^2)^1/2 = 7 x (2)^1/2
A boat is moving with a velocity 
with respect to the ground. The water in the river is moving with a velocity 
with respect to the ground. What is the relative velocity of boat with respect to river?- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
A boat is moving with a velocity with respect to the ground. The water in the river is moving with a velocity with respect to the ground. What is the relative velocity of boat with respect to river?
with respect to the ground. The water in the river is moving with a velocity with respect to the ground. What is the relative velocity of boat with respect to river?a)
b)
c)
d)
|
|
Suresh Reddy answered |
Velocity of boat wrt river = velocity of boat wrt ground - velocity of river wrt ground
I.e. v = (6i + 8j) - (-6i - 4j)
= 12i + 12j
I.e. v = (6i + 8j) - (-6i - 4j)
= 12i + 12j
A projectile is fired a velocity of 150 meters per second at an angle of 30 degrees with the horizontal. What is the magnitude of the vertical component of the velocity at the time the projectile is fired?- a)130 m/s
- b)75 m/s
- c)225 m/s
- d)150 m/s
Correct answer is option 'B'. Can you explain this answer?
A projectile is fired a velocity of 150 meters per second at an angle of 30 degrees with the horizontal. What is the magnitude of the vertical component of the velocity at the time the projectile is fired?
a)
130 m/s
b)
75 m/s
c)
225 m/s
d)
150 m/s
|
|
Nandini Patel answered |
The vertical component of the velocity is given by 150sin(30 ) =150X0.5 =75 m/s.
At what angle should a projectile with initial velocity ‘v’ be thrown, so that it achieves its maximum range?- a)450
- b)900
- c)600
- d)300
Correct answer is option 'A'. Can you explain this answer?
At what angle should a projectile with initial velocity ‘v’ be thrown, so that it achieves its maximum range?
a)
450
b)
900
c)
600
d)
300
|
Neha Joshi answered |
Sine of an angle has maximum value 1 when the angle is 90 degree Rmaxis obtained when 2ø = 90 degreeorø= 45 degree
Assertion: The maximum horizontal range of projectile is proportional to square of velocity.
Reason: The maximum horizontal range of projectile is equal to maximum height attained by projectile.- a)If both assertion and reason are true and the reason is the correct explanation of the assertion.
- b)If both assertion and reason are true but reason is not the correct explanation of the assertion.
- c)If assertion is true but reason is false.
- d)If the assertion and reason both are false.
- e)If assertion is false but reason is true.
Correct answer is option 'C'. Can you explain this answer?
Assertion: The maximum horizontal range of projectile is proportional to square of velocity.
Reason: The maximum horizontal range of projectile is equal to maximum height attained by projectile.
Reason: The maximum horizontal range of projectile is equal to maximum height attained by projectile.
a)
If both assertion and reason are true and the reason is the correct explanation of the assertion.
b)
If both assertion and reason are true but reason is not the correct explanation of the assertion.
c)
If assertion is true but reason is false.
d)
If the assertion and reason both are false.
e)
If assertion is false but reason is true.
|
|
Raghav Bansal answered |
when θ = 45º, Rmax ∝ u2
when θ = 90º, Hmax ∝ u2
It is clear that,
A particle is dropped from a height and another particle is thrown in horizontal direction with speed of 5 m/sec from the same height. The correct statement is:- a) Both particles will reach at ground simultaneously.
- b)Both particles will reach at ground with same speed.
- c)Particle will reach at ground first with respect to particle.
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
A particle is dropped from a height and another particle is thrown in horizontal direction with speed of 5 m/sec from the same height. The correct statement is:
a)
Both particles will reach at ground simultaneously.
b)
Both particles will reach at ground with same speed.
c)
Particle will reach at ground first with respect to particle.
d)
None of these
|
|
Preeti Iyer answered |
For both cases,
Because vertical downward component of velocity will be zero for both the particles.
Which one of the following is not an example of projectile?- a)A bullet fired from a gun.
- b)A kicked football.
- c)Taking off of an aircraft.
- d)A javelin thrown by an athlete.
Correct answer is option 'C'. Can you explain this answer?
Which one of the following is not an example of projectile?
a)
A bullet fired from a gun.
b)
A kicked football.
c)
Taking off of an aircraft.
d)
A javelin thrown by an athlete.
|
Top Rankers answered |
A projectile is any object thrown into space upon which the only acting force is gravity. A bullet fired from a gun, a kicked football, and a javelin thrown by an athlete are examples of projectiles once they are in motion and only gravity acts on them. Taking off of an aircraft is not a projectile because it involves continuous external force from the engines.
Pankaj and Sudhir are playing with two different balls of masses m and 2m, respectively. If Pankaj throws his ball vertically up and Sudhir at an angle θ, both of them stay in our view for the same period. The height attained by the two balls are in the ratio:- a)2 : 1
- b)1 : 1
- c)1 : cos θ
- d)1 : sec θ
Correct answer is option 'B'. Can you explain this answer?
Pankaj and Sudhir are playing with two different balls of masses m and 2m, respectively. If Pankaj throws his ball vertically up and Sudhir at an angle θ, both of them stay in our view for the same period. The height attained by the two balls are in the ratio:
a)
2 : 1
b)
1 : 1
c)
1 : cos θ
d)
1 : sec θ
|
|
Tejas Verma answered |
Time of flight for the ball thrown by pankaj, 
Time of flight for the ball thrown by sudhir,
According to problem,
Height of the ball thrown by pankaj,
Height of the thrown by sudhir,
Time of flight for the ball thrown by sudhir,
According to problem,Height of the ball thrown by pankaj,
Height of the thrown by sudhir,
A boy projects a stone vertically perpendicular to the trolley car with a speed v. If the trolley car moves with u constant velocity m, the time of flight of the stone is:- a)
- b)
- c)
- d)None of These
Correct answer is option 'B'. Can you explain this answer?
A boy projects a stone vertically perpendicular to the trolley car with a speed v. If the trolley car moves with u constant velocity m, the time of flight of the stone is:
a)
b)
c)
d)
None of These
|
|
Neha Sharma answered |
v = v0 sin θ
u = v0 cos θ
u = v0 cos θ
Time of flight depends on vertical component of velocity.
A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity?- a)47.3 km/hr, 23.4 km/hr
- b)48.3 km/hr, 22.4 km/hr
- c)49.3 km/hr, 21.4 km/hr
- d)46.3 km/hr, 24.4 km/hr
Correct answer is option 'C'. Can you explain this answer?
A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity?
a)
47.3 km/hr, 23.4 km/hr
b)
48.3 km/hr, 22.4 km/hr
c)
49.3 km/hr, 21.4 km/hr
d)
46.3 km/hr, 24.4 km/hr
|
|
Rahul Bansal answered |
Given,
Magnitude of displacement = 10 km
Total path length = 23 km
Time taken = 28 min = 7/15 hr.
Therefore,
Therefore, we can see that the average speed and magnitude of average velocity are not equal.
A man can swim with a speed of 4.0 km/h in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?- a)13 min, 700 m
- b)16 min, 650 m
- c)19 min, 500 m
- d)15 min, 750 m
Correct answer is option 'D'. Can you explain this answer?
A man can swim with a speed of 4.0 km/h in still water. How long does he take to cross a river 1.0 km wide if the river flows steadily at 3.0 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?
a)
13 min, 700 m
b)
16 min, 650 m
c)
19 min, 500 m
d)
15 min, 750 m
|
Stuti Kumar answered |
Explanation:
Speed of the man, vm = 4 km/h
Width of the river = 1 km
Width of the river = 1 km
The reason why cyclists bank when taking a sharp turn is- a)cyclists enjoy turning to one side and so bank
- b)to decelerate at the turns as turns are dangerous
- c)to supply the acceleration required to move fast
- d)to supply the sidewise (centripetal) acceleration required to make the direction change
Correct answer is option 'D'. Can you explain this answer?
The reason why cyclists bank when taking a sharp turn is
a)
cyclists enjoy turning to one side and so bank
b)
to decelerate at the turns as turns are dangerous
c)
to supply the acceleration required to move fast
d)
to supply the sidewise (centripetal) acceleration required to make the direction change
|
Tanvi Roy answered |
Explanation:In order to take a safe turn, the cyclist has to bend a little from his vertical position. In this case, a component of the reaction provides the required centripetal force.If q is angle made by the cyclist with the vertical then
In actual practice, the value of q is slightly less because the force of friction also contributes towards the centripetal force.
A sports car has a “lateral acceleration” of 0.96g = 9.4 m s−2. This is the maximum centripetal acceleration the car can sustain without skidding out of a curved path. If the car is traveling at a constant 40 m/s on level ground, what is the radius R of the tightest unbanked curve it can negotiate?- a)minimum radius = 160 m
- b)minimum radius = 170 m
- c)minimum radius = 180 m
- d)minimum radius = 175 m
Correct answer is option 'B'. Can you explain this answer?
A sports car has a “lateral acceleration” of 0.96g = 9.4 m s−2. This is the maximum centripetal acceleration the car can sustain without skidding out of a curved path. If the car is traveling at a constant 40 m/s on level ground, what is the radius R of the tightest unbanked curve it can negotiate?
a)
minimum radius = 160 m
b)
minimum radius = 170 m
c)
minimum radius = 180 m
d)
minimum radius = 175 m
|
Priya Deshpande answered |
Explanation:
The car is in uniform circular motion because it’s moving at a constant speed along a curve that is a segment of a circle. Hence we know
This is the minimum turning radius because arad is the maximum centripetal acceleration.
An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is:- a)1200 m
- b)0.33 km
- c)3.33 km
- d)33 km
Correct answer is option 'C'. Can you explain this answer?
An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is:
a)
1200 m
b)
0.33 km
c)
3.33 km
d)
33 km
|
|
Nandini Iyer answered |
Horizontal displacement of the bomb AB = Horizontal velocity × time available
In a harbor, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbor flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?- a)approximately north
- b)approximately north-east
- c)approximately east
- d)approximately south
Correct answer is option 'C'. Can you explain this answer?
In a harbor, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbor flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the north, what is the direction of the flag on the mast of the boat?
a)
approximately north
b)
approximately north-east
c)
approximately east
d)
approximately south
|
|
Ankita Patel answered |
Explanation:The flag is fluttering in the north-east direction. It shows that the wind is blowing toward the north-east direction. When the ship begins sailing toward the north, the flag will move along the direction of the relative velocity (vwb) of the wind with respect to the boat.
Hence, the flag will flutter approximately due east.
Which of the following statements not true?- a)The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point
- b)The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector
- c)The net acceleration of a particle in uniform circular motion is always along the radius of the circle towards the centre
- d)The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre
Correct answer is option 'D'. Can you explain this answer?
Which of the following statements not true?
a)
The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point
b)
The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector
c)
The net acceleration of a particle in uniform circular motion is always along the radius of the circle towards the centre
d)
The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre
|
Lead Academy answered |
Option A: True. The velocity vector of a particle at any point on its path is always tangent to the path at that point, as velocity represents the direction of motion.
Option B: True. For a particle in uniform circular motion, the centripetal acceleration points towards the center. Over one complete cycle, the acceleration vectors cancel out, resulting in an average acceleration of zero (null vector).
Option C: True. The net acceleration in uniform circular motion is centripetal acceleration, which always points towards the center of the circle along the radius.
Option D: Not true. This statement is incorrect because it implies that the net acceleration in all types of circular motion is always radial. While in uniform circular motion, the acceleration is purely radial, in non-uniform circular motion, there is an additional tangential component of acceleration due to the change in speed. Thus, the net acceleration in such cases is not always directed towards the center.
so that the resultant vector is a unit vector along the y-axis is
We can define the difference of two vectors A and B as the- a)sum of two vectors A and B' such that B' is equal to B multiplied by 0
- b)sum of two vectors A and B' such that B' is equal to B multiplied by -1
- c)sum of two vectors A and B' such that B' is equal to B multiplied by -2
- d)sum of two vectors A and B' such that B' is equal to B multiplied by 1
Correct answer is option 'B'. Can you explain this answer?
We can define the difference of two vectors A and B as the
a)
sum of two vectors A and B' such that B' is equal to B multiplied by 0
b)
sum of two vectors A and B' such that B' is equal to B multiplied by -1
c)
sum of two vectors A and B' such that B' is equal to B multiplied by -2
d)
sum of two vectors A and B' such that B' is equal to B multiplied by 1
|
Surbhi Mishra answered |
Explanation:
Vector subtraction is defined in the following way.
- The difference of two vectors, A - B , is a vector C that is, C = A - B
- The addition of two vector such that C = A + (-B). B has been taken in opposite direction.
Thus vector subtraction can be represented as a vector addition.
Which of the following statements is false for a particle moving in a circle with a constant angular speed?- a) The acceleration vector points to the centre of the circle.
- b) The acceleration vector is tangent to the circle.
- c)The velocity vector is tangent to the circle.
- d)The velocity and acceleration vectors are perpendiculai to each other.
Correct answer is option 'B'. Can you explain this answer?
Which of the following statements is false for a particle moving in a circle with a constant angular speed?
a)
The acceleration vector points to the centre of the circle.
b)
The acceleration vector is tangent to the circle.
c)
The velocity vector is tangent to the circle.
d)
The velocity and acceleration vectors are perpendiculai to each other.
|
|
Nandini Iyer answered |
In circular motion we know the velocity vector is tangent to the circle. If a particle moves in a circle with constant angular speed it perform uniform circular motion. In uniform circular motion the tangential acceleration of the particle is zero. The particle moves under radial acceleration only which points to the centre of the circle. Hence the velocity and acceleration vectors are perpendicular to each other.
Rain is falling vertically with a speed of 30 m s−1. A woman rides a bicycle with a speed of 10 m s−1 in the north to south direction. What is the direction in which she should hold her umbrella?- a)about 18∘ with the vertical, towards the south
- b)about 28∘ with the vertical, towards the south
- c)about 28∘ with the vertical, towards the north
- d)about 18∘ with the vertical, towards the north
Correct answer is option 'A'. Can you explain this answer?
Rain is falling vertically with a speed of 30 m s−1. A woman rides a bicycle with a speed of 10 m s−1 in the north to south direction. What is the direction in which she should hold her umbrella?
a)
about 18∘ with the vertical, towards the south
b)
about 28∘ with the vertical, towards the south
c)
about 28∘ with the vertical, towards the north
d)
about 18∘ with the vertical, towards the north
|
Jyoti Kapoor answered |
In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the woman.
v = vr + (-vc)
= 30 + (-10) = 20 m/s
tan θ = vc / vr = 10 / 30
θ = tan^-1 (1 / 3)
= tan^-1 (0.333) ≈ 18 degree
Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18 degree with the vertical.
A motorcycle stunt rider rides off the edge of a cliff. Just at the edge his velocity is horizontal, with magnitude 9.0 m/s. Find the magnitude of the motorcycle’s position vector after 0.50s it leaves the edge of the cliff.
- a)4.7 m
- b)5.2 m
- c)6.8 m
- d)7.2 m
Correct answer is option 'A'. Can you explain this answer?
A motorcycle stunt rider rides off the edge of a cliff. Just at the edge his velocity is horizontal, with magnitude 9.0 m/s. Find the magnitude of the motorcycle’s position vector after 0.50s it leaves the edge of the cliff.
a)
4.7 m
b)
5.2 m
c)
6.8 m
d)
7.2 m
|
Advait Ghoshal answered |
Explanation:The motorcycle’s x- and y-coordinates at t=0.50 s are
The negative value of y shows that the motorcycle is below its starting point.
The motorcycle’s distance from the origin at t=0.50 s is
Assertion: In projectile motion, the angle between the instantaneous velocity and acceleration at the highest point is 180∘.
Reason: At the highest point, velocity of projectile will be in horizontal direction only.- a)If both assertion and reason are true and the reason is the correct explanation of the assertion.
- b)If both assertion and reason are true but reason is not the correct explanation of the assertion.
- c)If assertion is true but reason is false.
- d)If the assertion and reason both are false.
- e)If assertion is false but reason is true.
Correct answer is option 'E'. Can you explain this answer?
Assertion: In projectile motion, the angle between the instantaneous velocity and acceleration at the highest point is 180∘.
Reason: At the highest point, velocity of projectile will be in horizontal direction only.
Reason: At the highest point, velocity of projectile will be in horizontal direction only.
a)
If both assertion and reason are true and the reason is the correct explanation of the assertion.
b)
If both assertion and reason are true but reason is not the correct explanation of the assertion.
c)
If assertion is true but reason is false.
d)
If the assertion and reason both are false.
e)
If assertion is false but reason is true.
|
|
Nandini Iyer answered |
At the highest point, vertical component of velocity becomes zero so there will be only horizontal velocity and it is perpendicular to the acceleration due to gravity.
A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is (∠POQ=40∘). 
- a)2v cos 40∘
- b)2v sin 40∘
- c)2v cos 20∘
- d)2v sin 20∘
Correct answer is option 'D'. Can you explain this answer?
A particle is moving on a circular path of radius r with uniform velocity v. The change in velocity when the particle moves from P to Q is (∠POQ=40∘).
a)
2v cos 40∘
b)
2v sin 40∘
c)
2v cos 20∘
d)
2v sin 20∘
|
|
Tanuja Kapoor answered |
Change in velocity:
The position vector of a particle is 
.The velocity of the particle is- a)Parallel to the position vector
- b)Perpendicular to the position vector
- c)Directed towards the origin
- d)Directed away from the origin
Correct answer is option 'B'. Can you explain this answer?
The position vector of a particle is .The velocity of the particle is
.The velocity of the particle isa)
Parallel to the position vector
b)
Perpendicular to the position vector
c)
Directed towards the origin
d)
Directed away from the origin
|
EduRev Class 9 answered |
As
therefore velocity of the particle is perpendicular to the position vector.
will be
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