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Two smooth balls A and B, each of mass m...

Two smooth balls A and B, each of mass m and radius R, have their centers at (0, 0, R) and at (5R, -R, R) respectively, in a coordinate system as shown. Ball A, moving along positive x axis, collides with ball B. Just before the collision, speed of ball A is 4m/s and ball B is stationary. The collision between the ball is elastic.

Impulse of the force exerted by A and B during the collision, is equal to

A

`(sqrt(3)mi+3mj)kg-m//s`

B

`((sqrt(3))/(2)mi-sqrt(3)mj)kg-m//s`

C

`(3mi-sqrt(3)mj)kg-m//s`

D

`(2sqrt(3)mi+3mj)kg-m//s`

Text Solution

Verified by Experts

The correct Answer is:
C
`vec(J)_(A on B) = m vec(v)_(B_(f))-vec(v)_(B_(i))`
`= m [4cos 30^(@)(cos 30 hat(i)-sin 30^(@)hat(j))-0]`
`= (2 mi - sqrt(3)mj kg - m//s)`
`therefore` (C )
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