Question

Two identical billiard balls strike a rigid wall with the same speed but at different angles and get reflected without any change in speed, as shown.

The ratio of the magnitudes of impulses imparted to the balls by the wall is

• A. $1.2$
• B. $1.6$
• C. $2.2$
• D. $2.6$

Answer 1

Answer: (A)

Case $ (i) $
$\left(p_{x}\right)=m u,\left(p_{y}\right)_{\text {initial }}=0$
$\left(p_{x}\right)_{\text {final }}=m u,\left(p_{y}\right)_{\text {final }}=0$
Impulse is the change in momentum vector.
$x-$ component of impulse $=-2 m u$
$y-$ component of impulse $=0$
Case $ (ii) $
$\left(p_{x}\right)_{\text {initial }}=m u \cos 30^{\circ} \,\,\,\left(p_{y}\right)_{\text {initial }}=-m u \sin 30^{\circ}$
$\left(p_{x}\right)_{\text {finel }}=-m u \cos 30^{\circ} \,\,\,\left(p_{y}\right)_{\text {final }}=m u \sin 30^{\circ}$
$x$ - Component of impulse $=-2 \,m u \cos 30^{\circ}$
$y$ Component of impulse $=0$
$\Rightarrow $ Ratio of magnitude of impulse
$=2 m u / 2 m u \cos 30^{\circ}=\frac{2}{\sqrt{3}}=1.2$