A particle of mass m is moving along the x -axis with initial velocity u i ^ . It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If sin   θ 1 = n sin   θ 2 then value of n is ________.

Question

A particle of mass m is moving along the x -axis with initial velocity u i ^ . It collides elastically with a particle of mass 10 m at rest and then moves with half its initial kinetic energy (see figure). If sin &#160; &#952; 1 = n sin &#160; &#952; 2 then value of n is ________.

Aicharya · Accepted Answer

From momentum conservation in perpendicular direction of initial motion.

{mv}_{1} {sinθ}_{1} = 10 {mv}_{2} {sinθ}_{2}

Given that

(\frac{1}{2} {mu}^{2}) \frac{1}{2} = \frac{1}{2} {mv}_{1}^{2} \dots \dots . (2)

From equation (1) & (2)

{sinθ}_{1} = \sqrt{10} {sinθ}_{2}

n = 10

A particle of mass m is moving along the x -axis with initial velocity u i ^ . It collides elastically with…

Solution