Motion in a Plane Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. If  then the value of  is
(a)
(b)
(c)
(d) A + B
2. A projectile is given an initial velocity of  m/s, where  is
along the ground and   is along the vertical. If  g = 10 m/s
2 
, the
equation of its trajectory is :
(a) y = x – 5x
2
(b) y = 2x – 5x
2
(c) 4y = 2x – 5x
2
(d) 4y = 2x – 25x
2
Page 2


PART-I (Single Correct MCQs)
1. If  then the value of  is
(a)
(b)
(c)
(d) A + B
2. A projectile is given an initial velocity of  m/s, where  is
along the ground and   is along the vertical. If  g = 10 m/s
2 
, the
equation of its trajectory is :
(a) y = x – 5x
2
(b) y = 2x – 5x
2
(c) 4y = 2x – 5x
2
(d) 4y = 2x – 25x
2
3. For a particle in uniform circular motion, the acceleration  at a point
P(R,?) on the circle of radius R is (Here ? is measured from the x-axis)
(a)
(b)
(c)
(d)
4. Six vectors,  and  have the magnitudes and directions
indicated in the figure. Which of the following statements is true?
(a)
(b)
(c)
(d)
5. Two particles start simultaneously from the same point and move along
two straight lines, one with uniform velocity v and other with a uniform
acceleration a. If a is the angle between the lines of motion of two
particles then the least value of relative velocity will be at time given by
(a)
Page 3


PART-I (Single Correct MCQs)
1. If  then the value of  is
(a)
(b)
(c)
(d) A + B
2. A projectile is given an initial velocity of  m/s, where  is
along the ground and   is along the vertical. If  g = 10 m/s
2 
, the
equation of its trajectory is :
(a) y = x – 5x
2
(b) y = 2x – 5x
2
(c) 4y = 2x – 5x
2
(d) 4y = 2x – 25x
2
3. For a particle in uniform circular motion, the acceleration  at a point
P(R,?) on the circle of radius R is (Here ? is measured from the x-axis)
(a)
(b)
(c)
(d)
4. Six vectors,  and  have the magnitudes and directions
indicated in the figure. Which of the following statements is true?
(a)
(b)
(c)
(d)
5. Two particles start simultaneously from the same point and move along
two straight lines, one with uniform velocity v and other with a uniform
acceleration a. If a is the angle between the lines of motion of two
particles then the least value of relative velocity will be at time given by
(a)
(b)
(c)
(d)
6. Initial velocity with which a body is projected is 10 m/sec and angle of
projection is 60°. Find the range R
(a)
(b)
(c)
(d)
7. A particle moves in a circle of radius 4 cm clockwise at constant speed
2 cm/s. If  and  are unit acceleration vectors along X and Y-axis
respectively (in cm/s
2
), the acceleration of the particle at the instant half
way between P and Q is given by
(a)
(b)
(c)
(d)
8. If vectors  and  are functions
of time, then the value of t at which they are orthogonal to each other is
Page 4


PART-I (Single Correct MCQs)
1. If  then the value of  is
(a)
(b)
(c)
(d) A + B
2. A projectile is given an initial velocity of  m/s, where  is
along the ground and   is along the vertical. If  g = 10 m/s
2 
, the
equation of its trajectory is :
(a) y = x – 5x
2
(b) y = 2x – 5x
2
(c) 4y = 2x – 5x
2
(d) 4y = 2x – 25x
2
3. For a particle in uniform circular motion, the acceleration  at a point
P(R,?) on the circle of radius R is (Here ? is measured from the x-axis)
(a)
(b)
(c)
(d)
4. Six vectors,  and  have the magnitudes and directions
indicated in the figure. Which of the following statements is true?
(a)
(b)
(c)
(d)
5. Two particles start simultaneously from the same point and move along
two straight lines, one with uniform velocity v and other with a uniform
acceleration a. If a is the angle between the lines of motion of two
particles then the least value of relative velocity will be at time given by
(a)
(b)
(c)
(d)
6. Initial velocity with which a body is projected is 10 m/sec and angle of
projection is 60°. Find the range R
(a)
(b)
(c)
(d)
7. A particle moves in a circle of radius 4 cm clockwise at constant speed
2 cm/s. If  and  are unit acceleration vectors along X and Y-axis
respectively (in cm/s
2
), the acceleration of the particle at the instant half
way between P and Q is given by
(a)
(b)
(c)
(d)
8. If vectors  and  are functions
of time, then the value of t at which they are orthogonal to each other is
:
(a)
(b)
(c) t = 0
(d)
9. A bus is moving on a straight road towards north with a uniform speed
of 50 km/hour turns through 90°. If the speed remains unchanged after
turning, the increase in the velocity of bus in the turning process is
(a) 70.7 km/hour along south-west direction
(b) 70.7 km/hour along north-west direction.
(c) 50 km/hour along west
(d) zero
10. The velocity of projection of oblique projectile is . The
horizontal range of the  projectile is
(a) 4.9 m
(b) 9.6 m
(c) 19.6 m
(d) 14 m
11. A particle crossing the origin of co-ordinates at time t = 0, moves in the
xy-plane with a constant acceleration a in the y-direction. If its equation
of motion is y = bx
2
 (b is a constant), its velocity component in the x-
direction is
(a)
(b)
(c)
Page 5


PART-I (Single Correct MCQs)
1. If  then the value of  is
(a)
(b)
(c)
(d) A + B
2. A projectile is given an initial velocity of  m/s, where  is
along the ground and   is along the vertical. If  g = 10 m/s
2 
, the
equation of its trajectory is :
(a) y = x – 5x
2
(b) y = 2x – 5x
2
(c) 4y = 2x – 5x
2
(d) 4y = 2x – 25x
2
3. For a particle in uniform circular motion, the acceleration  at a point
P(R,?) on the circle of radius R is (Here ? is measured from the x-axis)
(a)
(b)
(c)
(d)
4. Six vectors,  and  have the magnitudes and directions
indicated in the figure. Which of the following statements is true?
(a)
(b)
(c)
(d)
5. Two particles start simultaneously from the same point and move along
two straight lines, one with uniform velocity v and other with a uniform
acceleration a. If a is the angle between the lines of motion of two
particles then the least value of relative velocity will be at time given by
(a)
(b)
(c)
(d)
6. Initial velocity with which a body is projected is 10 m/sec and angle of
projection is 60°. Find the range R
(a)
(b)
(c)
(d)
7. A particle moves in a circle of radius 4 cm clockwise at constant speed
2 cm/s. If  and  are unit acceleration vectors along X and Y-axis
respectively (in cm/s
2
), the acceleration of the particle at the instant half
way between P and Q is given by
(a)
(b)
(c)
(d)
8. If vectors  and  are functions
of time, then the value of t at which they are orthogonal to each other is
:
(a)
(b)
(c) t = 0
(d)
9. A bus is moving on a straight road towards north with a uniform speed
of 50 km/hour turns through 90°. If the speed remains unchanged after
turning, the increase in the velocity of bus in the turning process is
(a) 70.7 km/hour along south-west direction
(b) 70.7 km/hour along north-west direction.
(c) 50 km/hour along west
(d) zero
10. The velocity of projection of oblique projectile is . The
horizontal range of the  projectile is
(a) 4.9 m
(b) 9.6 m
(c) 19.6 m
(d) 14 m
11. A particle crossing the origin of co-ordinates at time t = 0, moves in the
xy-plane with a constant acceleration a in the y-direction. If its equation
of motion is y = bx
2
 (b is a constant), its velocity component in the x-
direction is
(a)
(b)
(c)
(d)
12. The vector sum of two forces is perpendicular to their vector
differences. In that case, the forces
(a) cannot be predicted
(b) are equal to each other
(c) are equal to each other in magnitude
(d) are not equal to each other in magnitude
13. A water fountain on the ground sprinkles water all around it. If the
speed of water coming out of the fountain is v, the total area around the
fountain that gets wet is :
(a)
(b)
(c)
(d)
14. A stone projected with a velocity u at an angle ? with the horizontal
reaches maximum height H
1
. When it is projected with velocity u at an
angle  with the horizontal, it reaches maximum height H
2
. The
relation between the horizontal range R of the projectile, heights H
1
 and
H
2 
is
(a)
(b) R = 4(H
1
 – H
2
)
(c) R = 4 (H
1
 + H
2
)
(d)