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OneTime: Motion In Two Dimensions


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15 Questions MCQ Test Physics For JEE | OneTime: Motion In Two Dimensions

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OneTime: Motion In Two Dimensions - Question 1

A particle is projected from point O with velocity u in a direction making an angle α with the horizontal. At any instant its position is at point p at right angles to the initial direction of projection, Its velocity at point p is:

Detailed Solution for OneTime: Motion In Two Dimensions - Question 1

Horizontal velocity at point O = u cos α
Horizontal velocity at point P = v sin α

In projectile motion horizontal, component of velocity remains constant throughout the motion 
∴ v sin α = u cos α
⇒ v = u cot α

 

OneTime: Motion In Two Dimensions - Question 2

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:

Detailed Solution for OneTime: Motion In Two Dimensions - Question 2

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,

 

OneTime: Motion In Two Dimensions - Question 3

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.

.

Detailed Solution for OneTime: Motion In Two Dimensions - Question 3

Here we are given velocity of 'A', 
Velocity of 'A', w.r.t. 'B', 

Now,

Hence velocity of B, 

i.e. S of E

OneTime: Motion In Two Dimensions - Question 4

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:

Detailed Solution for OneTime: Motion In Two Dimensions - Question 4

v = vsin θ
u = vcos θ

Time of flight depends on vertical component of velocity.

OneTime: Motion In Two Dimensions - Question 5

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

Detailed Solution for OneTime: Motion In Two Dimensions - Question 5

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.

OneTime: Motion In Two Dimensions - Question 6

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).

 

Detailed Solution for OneTime: Motion In Two Dimensions - Question 6

Change in velocity:

OneTime: Motion In Two Dimensions - Question 7

A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following.

Detailed Solution for OneTime: Motion In Two Dimensions - Question 7

Due to constant velocity along horizontal and vertical downward force of gravity stone will hit the ground following parabolic path.

OneTime: Motion In Two Dimensions - Question 8

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:

Detailed Solution for OneTime: Motion In Two Dimensions - Question 8

Horizontal displacement of the bomb AB = Horizontal velocity × time available

*Multiple options can be correct
OneTime: Motion In Two Dimensions - Question 9

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.

Detailed Solution for OneTime: Motion In Two Dimensions - Question 9

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

Horizontal distance travelled by the ball from the edge of table, h = ut = 4 × 0.4 = 1.6 m

 

OneTime: Motion In Two Dimensions - Question 10

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:

Detailed Solution for OneTime: Motion In Two Dimensions - Question 10

For both cases,

Because vertical downward component of velocity will be zero for both the particles.

OneTime: Motion In Two Dimensions - Question 11

A projectile fired with initial velocity u at some angle θ has a range R. If the initial velocity be doubled at the same angle of projection, then the range will be:

Detailed Solution for OneTime: Motion In Two Dimensions - Question 11

If initial velocity be doubled then range will become four times.

OneTime: Motion In Two Dimensions - Question 12

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.

Detailed Solution for OneTime: Motion In Two Dimensions - Question 12

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.

OneTime: Motion In Two Dimensions - Question 13

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.

Detailed Solution for OneTime: Motion In Two Dimensions - Question 13


when θ = 45º, Rmax ∝ u2


when θ = 90º, Hmax ∝ u2

 

 It is clear that,

OneTime: Motion In Two Dimensions - Question 14

The radius vector describing the position of the particle A relative to origin.
2-D Kinematics/Motion in plane Problems with Solutions for JEE Main & JEE Advanced
Find the rectangular components of the average velocity in the time interval between t and t + Δ t.

Detailed Solution for OneTime: Motion In Two Dimensions - Question 14

*Multiple options can be correct
OneTime: Motion In Two Dimensions - Question 15

The radius vector describing the position of the particle A relative to origin.
2-D Kinematics/Motion in plane Problems with Solutions for JEE Main & JEE Advanced

Which of the following statements are true about the motion.

Detailed Solution for OneTime: Motion In Two Dimensions - Question 15


For these, it is clear that all the four options are correct

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