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NEET
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Physics
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Center of Mass, Momentum and Collision

NEET · Physics · Center of Mass, Momentum and Collision

A body A moving with momentum P collides one-dimensionally with...

A body AA moving with momentum PP collides one-dimensionally with another stationary body BB of same mass. During impact, AA gives impulse JJ to BB. Then which of the following is/are correct? (a) The total momentum of AA and BB is PP before and after impact and (P−J)(P-J) during the impact. (b) During the impact, BB gives impulse of magnitude JJ to AA. (c) The coefficient of restitution is (\left[\frac{2 J}{P}-1\right]). (d) The coefficient of restitution is (\left[\frac{2 J}{P}+1\right]).

Options

  1. AOnly (a) is correct.
  2. B(a) and (c) are correct.
  3. C(b) and (c) are correct.
  4. DOnly (c) is correct.

Correct answer

C. (b) and (c) are correct.

Step-by-step solution

According to the question, a collision between two bodies (AA and BB) is shown in the figure below, So, the coefficient of restitution (e= Relative velocity of separation  Relative velocity of approach ⇒e=J−pm+Jmpm−0=2JP−1(∵v=mvm=pm)\begin{aligned} e & =\frac{\text{ Relative velocity of separation }}{\text{ Relative velocity of approach }} \\ \Rightarrow \quad e & =\frac{\frac{J-p}{m}+\frac{J}{m}}{\frac{p}{m}-0}=\frac{2 J}{P}-1 \quad\left(\because v=\frac{m v}{m}=\frac{p}{m}\right) \end{aligned}) During the impact, BB gives impulse JB=p+J−p=JJ_B=p+J-p=J Hence, the statement (b) and (c) are correct.
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