The friction coefficient between plank and floor is `mu`. The man applies, the maximum possible force on the string and the system remains at rest. Then

Options

A. `T=(mu(m_(1)+m_(2)g))/(1+mu)`
B. `T=(mu(m_(1)+m_(2)g))/(1-mu)`
C. `T-mu(m_(1)+m_(2)g)`
D. `T=(mu(m_(1)+m_(2)g))/(1+mu)`

Answer

a

Explanation

If the man pulls down the string with maximum force T, the man experiences force T upward. Taking `m_(1)` and `m_(2)` as a system, normal force between plank and ground is `N=(m_(1)+m_(2))g-T` For plank to stay at rest, if the man is exerting the maximum force then frictional force will act at its maximum value. For equilibrium `T=muN`
`T=mu(m_(1)g+m_(2)g-T) rarr T=(mu(m_(1)+m_(2)))/(1+mu)` g