Two masses `m` and `M` are attached with strings as shown. For the system to be in equilibrium we have.

Options

A. `tantheta=1+(2M)/(m)`
B. `tantheta=1+(2m)/(M)`
C. `tantheta=1+(M)/(2m)`
D. `tantheta=1+(m)/(2M)`

Answer

A

Explanation

For the smooth upper half, (2l= length of incline)
`v^(2)-u^(2)=2aS`
`v^(2)-0=2gsin theta l`
`v=sqrt(2gsin thetal)`
For the lower half,
`v^(2)-u^(2)=2aS`
`0-2g sin theta l =- 2g(mucos theta-sin theta)l`
`sintheta=mucos theta-sintheta`
`mu=2tan theta`