Two balls of same mass are released simultaneously from heights h & 2h from the ground level. The balls collide with the floor & stick to it. Then the velocity-time graph of centre of mass of the two balls is best represented by :

Options

A.
B.
C.
D.

Answer

B

Explanation

`(B)` As both the balls are released simultaneously, at any instant before the lower balls reaches the ground bothe have the same velocity`,v=gt i.e.,'v' vs. 't'` is a straight line graph.
`V_(CM)=(mv(t)+mv(t))/(2m)=v(t),v(t)` beingh the instantaneous velocity.
Just after the lower ball strikes ground and comes to rest `:`
`V_(CM)=(mv(t))/(2m)=(v(t))/(2)`
`i.e.` the velocity suddently drops to half its value.
Hence graphs `(A) & (B)` are chosen.
After collision `:`
`a_(CM)=(m(g)+m(0))/(m+m)=(g)/(2)`
`i.e.` the slope `(` of `v-t` curve `)` should decrease to half. Hence `(B)` is the best option.