Two sphere `A and B` of masses `m_(1) and m_(2)` respectivelly colides. A is at rest initally and `B` is moving with velocity `v` along x-axis. After collision `B` has a velocity `(v)/(2)` in a direction perpendicular to the original direction. The mass `A` moves after collision in the direction.

Options

A. `theta = tan^(-1) (-1/2) ` to the X - axis
B. same as that of B
C. opposite to that of B
D. `theta = tan^(-1) (1/2) ` to the X - axis

Answer

D

Explanation

Momentum conserved ,along X - direction
`m_(2)u_(1)+m_(1)u_(2) = m_(2)(0) +m_(1)v_(2) cos theta `
`m_(2)v = m_(1)v_(2) cos theta `
`(m_(2))/(m_(1)) v = v_(2) cos theta " " …(i)`
Momentu conerved along Y - direction
` 0+0 = m_(2)v_(1)-m_(1)v_(2)sin theta `
`(m_(2))/2 v = m_(1)v_(2) sin theta `
`((m_(2))/m_(1)v/2 )= v_(2) sin theta " " ...(ii)`
Divide equation (ii) by (i)
`tan theta =1/2 rArr 1 = tan^(-1) (1//2)`
But `theta ` is in anticlockwise direction so takes as negative
Angle ` = - theta = - tan (1/2)`
`tan((-1)/2)` (along + X direction )