In the given situation, what is the minimum mass of block A so that block B remains stationary with respect to the wall? The coefficient of friction is `mu` between wall and block. All other surfaces are smooth.

Options

A. `((M + m))/(mu + 1)`
B. `(M)/(mu - 1)`
C. `(M + m)/(mu)`
D. `((M + m))/(mu - 1)`

Answer

D

Explanation

N = ma (i)
F = mg (ii)
m'g - T - m 'a (iii)
T - N = Ma (iv)
Solving (i) and (ii)
`mu N = mg` or `mu m a = mg` `implies a = (g)/(mu)`
adding (i), (iii) and (iv)
`m 'g = (m + m ' + M) (g)/(mu)` `implies m 'g - (m 'g)/(mu) = (m + M) (g)/(mu)`
`m (mu - 1) = (m + M)` `implies m ' = (m + M)/((mu - 1))`