A smooth sphere is moving on a horizontal surface with velocity vector 3 i + j immediately before it hits a vertical wall. The wall is parallel to the vector j and the coefficient of restitution between the wall and sphere is 1 3 . The velocity vector of the sphere after it hits the wall is

A smooth sphere is moving on a horizontal surface with velocity v…

MCQ

A smooth sphere is moving on a horizontal surface with velocity vector $3 \hat i + \hat j$ immediately before it hits a vertical wall. The wall is parallel to the vector $\hat j$ and the coefficient of restitution between the wall and sphere is $\frac{1}{3}$. The velocity vector of the sphere after it hits the wall is

A
$\hat i + \hat j$
B
$3 \hat i - \frac{1}{3} \hat j$
✓
$-\hat i + \hat j$
D
$\hat i - \hat j$

✓

Answer

Correct option: C.

$-\hat i + \hat j$

c
$y-component$ of velocity is parallel to wall so it will not change velocity of sphere $=-v \hat{i}+\hat{j}$

$\mathrm{e}=\frac{\mathrm{V}_{\text {sepration }}}{\mathrm{V}_{\text {approach }}} \Rightarrow \frac{1}{3}$

$\frac{V}{3}=\frac{1}{3}$

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