A circular disc of mass `'2m'` and radius `'3r'` is resting on a flat frictionless surface. Another circular disc of mass m and radius `'2r'`, moving with a velocity `'u'`. hits the first disc as shown in the figure. The collision is elastic.

What is the magnitude of normal component of final velocity of the smaller disc'?

Options

A. `u/5`
B. `(2u)/512`
C. `(3u)/5`
D. `(4u)/5`

Answer

A

Explanation

Tangential component `=usintheta=4u/5`
along normal velocity of m before collision:
`u_(1)=ucostheta=(3u)//5`

Along normal `mv_(1)+2mv_(2)="mu"_(1)`
`(v_(2)-v_(1))/u_(1)=1`
solve to get `v_(1)=-u/5,v_(2)=(2u)/5`