This question has Statement - I and Statement - II of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I: A point particle of mass m moving with speed ν collides with stationary point particle of mass M . If the maximum energy…

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This question has Statement - I and Statement - II of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I: A point particle of mass m moving with speed &#957; collides with stationary point particle of mass M . If the maximum energy loss possible is given as f 1 2 m &#957; 2 then f = m M + m . Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.

Aicharya · Accepted Answer

Maximum energy loss will take place in perfectly inelastic collision, and is given by, $∆ K = \frac{P^{2}}{2 m} - \frac{P^{2}}{2 (m + M)}$
$\Rightarrow ∆ K = \frac{P^{2}}{2 m} [1 - \frac{m}{(m + M)}]$
$\Rightarrow ∆ K = \frac{P^{2}}{2 m} [\frac{M}{(m + M)}]$
$\Rightarrow ∆ K = \frac{1}{2} m v^{2} [\frac{M}{(m + M)}]$
On comparing with the given form of equation, we have, $(f = \frac{M}{m + M})$

Hence Statement- $I$ is false, Statement- $II$ is true. ( As it is perfect Inelastic collision)

This question has Statement - I and Statement - II of the four choices given after the Statements, choose…

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