A particle of mass m is moving along the x-axis with initial velocity ui . 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 theta _(1) = sqrt(n) sin theta_(2)` then value of n is

Answer

10

Explanation

`1/2 mv_(1)^(2) = 1/2 (1/2 "mu"^(2))`
` v_(1)^(2) = (u^(2))/2 `
` v_(1) = u/(sqrt(2)) " " ….(i)`
Also , ` 1/2 "mu"^(2) = 1/2 mv_(1)^(2) +1/2 (10 m) xx v_(2)^(2)`
` 1/2 xx 10 m xx v_(2)^(2) = 1/2 xx1/2 "mu"^(2)`
`v_(2)^(2) = (u^(2))/20 ` or , `v_(2) = u/(sqrt(20))`
now , `mv_(1) sin theta_(1) = 10 mv_(2) sin theta _(2)`
`u/(sqrt(2)) sin theta_(1) = 10 xx u/(sqrt(20)) sin theta_(2)`
` sin theta _(1) = 10/(sqrt(10) sin theta_(2)`
`sin theta_(1) = sqrt(10) sin theta_(2)`
` :. n = 10 `