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Q.

A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to +ve y-axis and intersecting z-axis at z = a in figure.

The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is

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a

$m v a \hat{i}$

b

$2 m v a \hat{i}$

c

$m v y \hat{i}$

d

$2 m v y \hat{i}$

answer is B.

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Detailed Solution

$\bar{L} = \bar{r} \times \bar{p}$

${\bar{L}}_{1} = (a \bar{k}) \times (m v \bar{j})$

= (mva) x - $\bar{i}$

${\bar{L}}_{2} = (a \bar{k}) \times (m v \times - \bar{j})$ = (mva) $\bar{i}$

$L_{2} - L_{1} = m v a \times 2 \bar{i}$

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