Question

A ball of mass m moving with a velocity v undergoes an oblique elastic collision with another ball of the same mass m but at rest. After the collision, if the two balls move with the same speeds, the angle between their directions of motion will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Refer to Figure

Taking the components of the velocities along x and y – axes and using the law of conservation of momentum for x and y components we have
$mu=mvcos{\theta }_1+mvcos{\theta }_2\dots \dots \left(i\right)$
and $0=mvsin{\theta }_1-mvsin{\theta }_2\dots \dots \left(ii\right)$
From (ii) we get $sin{\theta }_1=sin{\theta }_{2}or{\theta }_1={\theta }_2$.
Using ${\theta }_1={\theta }_2=\theta$ in (i) we have
$mu=2mvcos\theta$
or $cos\theta =\frac{u}{2v}$
Since the collision is elastic, kinetic energy is also conserved, i.e.
$\frac{1}{2}m{u}^2=\frac{1}{2}m{v}_1^2+\frac{1}{2}m{v}_2^2$
or $u^2=2v^{2}oru=\sqrt{2}v\dots \dots \left(iv\right)$
Using (iv) and (iii) we have $cos\theta =\frac{1}{\sqrt{2}}or\theta ={45}^{\circ }$. Thus ${\theta }_1+{\theta }_2=2\theta ={90}^{\circ }$. Hence the correct choice is (c).