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

MCQ

$A$ smooth sphere is moving on a horizontal surface with a velocity vector $(\,2\,\hat i + 2\,\hat j\,)$ $m/s$ immediately before it hit a vertical wall. The wall is parallel to vector $\hat j$ and coefficient of restitution between the sphere and the wall is $e = 1/2$ . The velocity of the sphere after it hits the wall is

A
$\,\hat i - \,\hat j$
✓
$ - \,\hat i + 2\,\hat j$
C
$ - \,\hat i - \,\hat j$
D
$2\,\hat i - \,\hat j$

✓

Answer

Correct option: B.

$ - \,\hat i + 2\,\hat j$

b
Initial velocity of the sphere $u=2 \hat{i}+2 \hat{j}$ As the wall is parallel to $y$ axis, thus its velocity componant in $y$ direction remains the same i.e $2 \hat{j}$ but its velocity componant in $x$ direction changes.

Newtons law of collision in $x$ direction: $\quad \frac{-v^{\prime}-0}{v-0}=-e$

$\frac{v^{\prime}-0}{2 \hat{i}-0}=-\frac{1}{2} \quad \Longrightarrow \quad v^{\prime}=-\hat{i}$

$\Longrightarrow$ velocity vector of sphere after hitting the wall $\quad u^{\prime}=-\hat{i}+2 \hat{j}$

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