Find the maximum value of (m//m) in the situation shown in figure so that the system remains at rest. Friction coefficient of both the contacts is `mu` , string is massless an pulley is friction less.

Options

A. `(costheta)/(sintheta-mucostheta)`
B. `(sintheta)/(sintheta-mucostheta)`
C. `(mucostheta)/(sintheta-mucostheta)`
D. `(mu)/(sintheta-mucostheta)`

Answer

D

Explanation

The system is at rest `(F_(net)=0)`
For maximum `M//m` , Limiting friction will be acting on both blocks (at contact surface).
`F=Net` pulling force on the whole system
`mumg+muMgcostheta=Mgsintheta`
`Mg(sintheta-mucostheta)=mumg`
`(M)/(m)=(mu)/((sintheta-mucostheta))`