A simple pendulum , made of a string of length l and a bob of mass m, is released from a small angle `theta_(0)` it strikes a block of mass M, kept on a horizontal surface at its lowest point of oscil,ations , elastically , it bounces back and goes up to an angle `theta)(1-)` then M is given by :

Options

A. `m/2((theta_(0)+theta_(1))/(theta_(0)-theta_(1)))`
B. `m((theta_(0)-theta_(1))/(theta_(0)+theta_(1)))`
C. `m((theta_(0)+theta_(1))/(theta_(0)-theta_(1)))`
D. `m/2((theta_(0)-theta_(1))/(theta_(0)+theta_(1)))`

Answer

B

Explanation

`omega=sqrt(g/l)`
Velocity just befor collsion
`u=(sqrt(g/1) theta_(0)) 1=sqrt(gltheta_(1))`
Momentum conservation:
`("mu")=Mv'-mv` …(i)
e=1:
`v'+v=u` …(ii)
From (i)and(ii)
`m(u+v)=M(u-v)`
`m(theta_(0)+theta_(1))=M(theta_(0)-theta_(1))`
`M=m((theta_(0)+theta_(1))/(theta_(0)-theta_(1)))`