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 different speeds, then the angle between their directions of motion will be

Answer 1

answer : 90°

explanation : Let us consider component of velocities along x - axis and y - axis and using the law of conservation of linear momentum for x and y components we have ,

along x - axis,

$mu=mvcos\theta_1+mvcos\theta_2$.....(1)

along Y-axis,

$0=mvsin\theta_1-mvsin\theta_2$....(2)

From equation (2),

we get, $\theta_1=\theta_2=\theta(Let)$

putting it in equation (1),

$mu=2mvcos\theta$

so, $cos\theta=\frac{u}{2v}$

since collision is elastic so kinetic energy is also conserved.

i.e., 1/mu² = 1/2mv² + 1/2mv²

or, u² = 2v²

or, u = √2v

so, $cos\theta=\frac{1}{\sqrt{2}}$

$\implies\theta=45^{\circ}$

now angle between their direction of motion is $\theta_1+\theta_2=2\theta=90^{\circ}$

Answer 2

Answer:

90.................