1. A bullet fired into a fixed target loss half of its velocity after penetrating 3cm. How much further will it penetrate before coming to rest assuming that it faces constant resistance in motion?
a) 1.5cm
b) 1cm
c) 3cm
d) 2cm
Explanation: If u is initial velocity then v=u/2 s=3cm
As v2-u2=2as
a = -u2/8
Now v=0
Initial velocity=u/2
s=1cm
Thus the bullet will penetrate a further distance of 1cm before coming to rest.
2. From a building 2 balls A and B are thrown such that A is thrown upward and B is thrown downward. If vA and vB are their respective velocities on reaching the ground, then _____________
a) vB is greater than vA
b) vB = vA
c) vB is lesser than vA
d) Their velocities depend on their masses.
Explanation: Suppose the ball A is thrown upward with velocity u and ball B is thrown downward with same velocity u. After reaching the highest point the ball A comes back to its position with the same velocity in downward direction. As the 2 balls fall from the same position with the same velocity, both attain the same velocity on reaching the ground.
3. The displacement of the body is given to be proportional to the cube of time elapsed. The magnitude of acceleration of body is ____________
a) Increasing with time
b) Decreasing with time
c) Constant but not zero
d) Zero
Explanation: s=kt3
Velocity=ds/dt=3kt2
Acceleration=dv/dt=6kt
Clearly acceleration increases uniformly with time.
4. When a ball is thrown vertically upwards, at the maximum height ____________
a) The velocity is zero and therefore there is no acceleration acting in the particle
b) The acceleration is present and therefore the velocity is not zero
c) Acceleration depends on the velocity
d) Acceleration is independent of the velocity
Explanation: When a ball is thrown vertically upward, at the maximum height the acceleration becomes independent of the velocity.
5. Tom and Jerry are running forward at the same speed. They are following a rubber ball at a constant speed v as seen by the thrower. According to Sam, who’s standing on the ground, the speed of the ball is ____________
a) Same as v
b) Greater than v
c) Less than v
d) Zero
Explanation: As they are moving in the same direction, the relative velocity of the ball with respect to Tom or Jerry will be
vB=v+v(Tom or Jerry)
For Sam, the speed of the ball will be greater than v.
6. For motion in two or three dimensions, what is the angle between velocity and acceleration vectors?
a) 0°
b) 180°
c) Between 0° and 180°
d) 90°
Explanation: For motion in one dimension, the velocity and acceleration are always along the same line either in the same direction or in opposite direction. For motion in two or three dimensions, the angle between velocity and acceleration vectors may have any value between 0° and 180°.
7. A cyclist moves along a circular path of radius 70m. If he completes one round in 11s, calculate the total length of a path.
a) 40m
b) 440m
c) 0m
d) 11m
Explanation: Radius of the circular path, r = 70m
Time takes to complete one round, t = 11s
Total length of the path, s = 2πr = 2×22/7×70 = 440m.
8. An object thrown from an aeroplane is an example for ____________
a) Projectile motion
b) Resolution of forces
c) Composition of vectors
d) Addition of vectors
Explanation: A projectile is a name given to anybody which once thrown into space with some initial velocity, moves thereafter under the influence of gravity alone without being propelled by an engine or fuel. The path followed by a projectile is called its trajectory.
9. A ball is dropped downward from the roof of a building and simultaneously another ball is thrown in a horizontal direction, when will the balls reach the ground?
a) Same time and same place
b) The first ball will reach later than the second ball
c) The second ball will reach later than the second ball
d) Same time but different places
Explanation: Both the balls will reach the ground at the same time but at different places. The vertical motion is not affected by the horizontal motion. This is called the principle of physical independence.
10. A body is projected horizontally from the top of a cliff with a velocity of 9.8m/s. What time elapses before horizontal and vertical velocities become equal? Take g = 9.8m/s2
a) 9.8s
b) 0s
c) 10s
d) 1s
Explanation: Horizontal velocity at any instant, vx = u = 9.8m/s
Vertical velocity at any instant, vy = 0 + gt = 9.8t
9.8 = 9.8t
t = 1s.