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(D) In a perfectly inelastic collision,the particles stick together and move with a common velocity $V_f = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$.Since th

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Statement-$1$ is true,Statement-$2$ is true. Statement-$2$ is not the correct explanation of Statement-$1$.

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(D) In a perfectly inelastic collision,the particles stick together and move with a common velocity $V_f = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$.Since the system retains a common velocity after the collision,the final kinetic energy $K_f = \frac{1}{2}(m_1 + m_2)V_f^2$ is not zero.Thus,Statement-$1$ is true because the system does not lose all its energy.Statement-$2$ is also true because the law of conservation of linear momentum is a fundamental principle that applies to all collisions in the absence of external forces.However,the conservation of momentum (Statement-$2$) is not the reason why some kinetic energy is retained (Statement-$1$); the retention of energy is due to the requirement of momentum conservation in a system that must move together.Therefore,Statement-$1$ and Statement-$2$ are both true,but Statement-$2$ is not the correct explanation of Statement-$1$.

Find the correct option based on the two statements given below.
Statement-$1$ : Two particles moving in the same direction do not lose all their energy in a perfectly inelastic collision.
Statement-$2$ : The law of conservation of linear momentum is obeyed for all types of collisions.

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Statement $1$: In a perfectly inelastic collision,the total energy of two particles moving in the same direction is not completely lost.
Statement $2$: The principle of conservation of momentum is valid for all types of collisions.

$A$ bullet of mass $a$ moving with velocity $b$ strikes a block of mass $c$ and gets embedded in it. Find the velocity of the block.

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Find the correct option based on the two statements given below.Statement-$1$ : Two particles moving in the same direction do not lose all their energy in a perfectly inelastic collision.Statement-$2$ : The law of conservation of linear momentum is obeyed for all types of collisions.