Question

Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement 2 : Principle of conservation of momentum holds true for all kinds of collisions.

A: Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
B: Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
C: Statement-1 is false, Statement-2 is true.
D: Statement-1 is true, Statement-2 is false.

Answer 1

Hint: An inelastic collision is a collision in which there is a loss of kinetic energy. The momentum of the system is conserved in an inelastic collision, kinetic energy is not conserved. That is because here some kinetic energy had been transferred to something else. Such collisions are simply called inelastic collisions.

Complete answer:
An inelastic collision arises when two of the objects collide with each other. Momentum is conserved, because the total momentum of both objects before and after collision is the same. Some of the kinetic energy is converted to some other forms.
In an elastic collision, total kinetic energy and the total momentum before and after collision are the same.
The inelastic collisions are non- conservative in nature.
Let us consider two particles of masses ${{m}_{1}}$ and ${{m}_{2}}$ moving with velocities ${{u}_{1}}$ and ${{u}_{2}}$ respectively before collision. If there velocities after collision are ${{v}_{1}}$ and ${{v}_{2}}$, then according to conservation of momentum we have,
${{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}$
Here, the initial and final positions are widely separated so that the interaction forces between the particles becomes effectively zero. Hence the potential energy before and after remains the same. If the collision is perfectly elastic, the total kinetic energy of the particles is not changed by the collision.
$\dfrac{1}{2}{{m}_{1}}u_{1}^{2}+\dfrac{1}{2}{{m}_{2}}u_{2}^{2}=\dfrac{1}{2}{{m}_{1}}v_{1}^{2}+\dfrac{1}{2}{{m}_{2}}v_{2}^{2}$
According to the kinetic theory of gases, such elastic collisions occur between the molecules of a gas. This type of collision mostly takes place between atoms, electrons and protons.
In case of inelastic collision, a part of kinetic energy is converted to some other forms. This energy appears in the form of thermal energy in macroscopic particles.
Both statements are correct. But the correct explanation of statement 1 is that the whole phenomenon is happening due to the conservation of linear momentum.

So, the correct answer is “Option B”.

Note:
The principle of conservation of momentum states that if objects collide, the total momentum before the collision is the same as the total momentum after collision if there are no external forces. . The momentum of the system is conserved in an inelastic collision, kinetic energy is not conserved. This is because here some kinetic energy had been transferred to something else.