Kinematics of Machinery Questions and Answers Part-7

1.The wheels of a moving car possess
a) potential energy only
b) kinetic energy of translation only
c) kinetic energy of rotation only
d) kinetic energy of translation and rotation both.

Answer: d
Explanation: in the locomotive driving wheels and wheels of a moving car, then the total kinetic energy of the body is equal to the sum of kinetic energies of translation and rotation.

2. The bodies which rebound after impact are called
a) inelastic bodies
b) elastic bodies
c) solid bodies
d) none of the mentioned

Answer: b
Explanation: The bodies, which rebound after impact are called elastic bodies and the bodies which does not rebound at all after its impact are called inelastic bodies.

3. The coefficient of restitution for inelastic bodies is
a) zero
b) between zero and one
c) one
d) more than one

Answer: a
Explanation: The process of regaining the original shape is called restitution. Inelastic bodies can not regain their original shapes. Therefore their coefficient of restitution is zero.

4. Which of the following statement is correct ?
a) The kinetic energy of a body during impact remains constant.
b) The kinetic energy of a body before impact is equal to the kinetic energy of a body after impact.
c) The kinetic energy of a body before impact is less than the kinetic energy of a body after impact.
d) The kinetic energy of a body before impact is more than the kinetic energy of a body after impact

Answer: d
Explanation: Total kinetic energy of the system before impact,
E1 = 1/2 m1 (u1)2 + 1/2 m2 (u2)2
When the two bodies move with the same velocity v after impact, then
Kinetic energy of the system after impact,
E2= 1/2( m1 + m2) v2
Loss of kinetic energy during impact,
EL = E1 – E2

5. A body of mass m moving with a constant velocity v strikes another body of same mass m moving with same velocity but in opposite direction. The common velocity of both the bodies after collision is
a) V
b) 2 V
c) 3 V
d) 4 V

Answer: b
Explanation: If the body will move in opposite direction a negative sign would be there.
We know that Common velocity = V12
Here both the velocities are same.
Therefore Common velocity = V – (-V)
= V + V = 2V

6. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the loss of kinetic energy when the collision is inelastic.
a) 18.75 N-m
b) 19.75 N-m
c) 17.75 N-m
d) 16.75 N-m

Answer: a
Explanation: Loss of kinetic energy during inelastic collision is given by
m1m2/(2(m1+ m2) (u12 – u22)
substituting the values we get
El = 18.75 N-m.

7. The coefficient of restitution is 0 for a completely inelastic collision.
a) true
b) false

Answer: a
Explanation: For a completely inelastic collision the bodies stick to each other after collision, hence there is no relative velocity after collision therefore the coefficient of restitution is 0.

8. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the loss of kinetic energy when the collision is inelastic with e = 0.6.
a) 18.75 N-m
b) 12.00 N-m
c) 13.75 N-m
d) 12.75 N-m

Answer: b
Explanation: Loss of kinetic energy during inelastic collision with coefficient of restitution is given by
m1m2/(2(m1+ m2) (u12 – u22)(1-e2))
substituting the values we get
El = 12 N-m.

9. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the common velocity in m/s after collision when the collision is completely inelastic
a) 2.5
b) 9.75
c) 7.25
d) 9.75

Answer: a
Explanation:ommon velocity during inelastic collision is given by
m1u1 + m2u2/(m1+ m2) = v
substituting the values we get
V = 2.5 m/s

10. A sphere of mass 25 Kg is moving at a speed of 1.5 m/s undergoes collision with another sphere of mass 50 Kg moving at 3m/s in the same direction, find the velocity of 50 Kg mass in m/s after collision when the collision is elastic
a) 2.5
b) 2.00
c) 7.25
d) 6.75

Answer: b
Explanation: Velocity during elastic collision is given by
m1u1 + m2u2/(m1+ m2) = v
substituting the values we get
V = 2.5 m/s
v1 = 2V – u1
v1 = 2m/s