Free Collisions MCQs with Answers

1. A body of mass 2 kg moving at 3 m s-1 collides and sticks to a stationary body of mass 4 kg. The common velocity after impact is

• A. 0.5 m s-1
• B. 1 m s-1
• C. 1.5 m s-1
• D. 2 m s-1

Explanation: Momentum is conserved, so the initial momentum of 2 times 3, which is 6 kg m s-1, is shared by the combined mass of 6 kg, giving a velocity of 1 m s-1. This is a perfectly inelastic collision, so kinetic energy is not conserved even though momentum is. Only the moving body contributes momentum, since the other starts at rest.

2. In an elastic collision, which quantity is conserved in addition to momentum?

• A. Kinetic energy
• B. Mass alone
• C. Velocity of each body
• D. Potential energy

Explanation: An elastic collision is defined by the conservation of kinetic energy as well as momentum, and collisions between gas molecules are treated this way. In an inelastic collision momentum is still conserved but some kinetic energy is converted into heat, sound or deformation. Individual velocities change in every collision.

3. In an isolated system, the total linear momentum

• A. always increases
• B. is conserved, whatever type of collision occurs
• C. is conserved only in elastic collisions
• D. is zero

Explanation: Momentum conservation follows from Newton's third law and holds in every collision and explosion provided no external force acts, whether the collision is elastic or not. Kinetic energy, by contrast, is conserved only in a perfectly elastic collision. This distinction is what most collision questions are really testing.

4. In a perfectly inelastic collision, the two bodies

• A. bounce apart with no loss of kinetic energy
• B. stick together and move with a common velocity, losing some kinetic energy
• C. conserve kinetic energy but not momentum
• D. come to rest

Explanation: Momentum is still conserved, so the common velocity follows from the total momentum divided by the total mass, but some kinetic energy is converted to heat, sound and deformation. A bullet embedding in a block is the standard example. The bodies come to rest only in the special case where the total momentum happens to be zero.

5. A body of mass 2 kg moving at 3 m per second collides and sticks to a stationary body of mass 4 kg. Their common velocity is

• A. 1 m per second
• B. 1.5 m per second
• C. 0.5 m per second
• D. 3 m per second

Explanation: Total momentum before is 2 multiplied by 3, that is 6 kg m per second, and the combined mass afterwards is 6 kg, so the common velocity is 1 m per second. The kinetic energy falls from 9 J to 3 J, the difference going into heat and deformation. Momentum is conserved even though energy is not.

6. In an elastic collision between two bodies of equal mass, one moving and one at rest

• A. they stick together
• B. the moving body stops and the stationary one moves off with the original velocity
• C. both move off at half the original velocity
• D. the moving body rebounds

Explanation: Conserving both momentum and kinetic energy for equal masses gives a complete exchange of velocities, which is what makes the Newton's cradle behave as it does and why a cue ball stops dead on a full head on strike. Sticking together would violate energy conservation for an elastic collision. Both moving off at half speed conserves momentum but not kinetic energy.

7. If a body having mass m1 (2 kg) moving with 5 m/s approaches another mass m2 (3 kg) with speed of 1 m/s in same direction, relative speed of approach is 4 m/s. Relative speed of separation after collision will be:

• A. 4 m/s
• B. 2 m/s
• C. 6 m/s
• D. Depends on masses

Explanation: For a perfectly elastic collision the relative speed of separation equals the relative speed of approach, whatever the masses, which follows from conserving both momentum and kinetic energy. So the 4 m per second closing speed becomes a 4 m per second separating speed. In an inelastic collision the separation speed would be smaller, and in a perfectly inelastic one it would be zero.