A spherical ball of mass `M` moving with initial velocity `V` collides elastically with another ball of mass `M`, which is fixed at one end of `L` shaped rigid massless frame as shown in Fig. (a). The `L` shaped frame contains another mass `M` connected at the other end.

How soon will the frame come to the orientation shown in Fig. (b) after collision?

Options

A. `(pil)/(4v)`
B. `(7pil)/(8v)`
C. `(pil)/v`
D. `(7pil)/(2v)`

Answer

D

Explanation

Applying conservation of momentum
`Mv_(1)+2Mv_(c)=mu`
`v_(1)+2v_(c)=u`…………..i
`e=1=(v_(c)+(omegal)/2cos45^@-v_(1))/(u-0)`
`u=v_(c)+(omegal)/2-v_1`………ii

Applying conservation of angular momentum about `FC`
`Mv_(1)l/2+2M(l/(sqrt(2)))^(2)omega="Mu"l/2`
`v_(1)+2omegal=u`.............iii
Solving eqn i, ii and iii we get `v_(1)=-u/7,omega=(4u)/(7l)`
Angle rotated `theta=pi`
`t=theta/omega=(7pil)/(4u)`