Two blocks `M` and `m` are arranged as shown in the diagram The coefficient of friction between the block is `mu_(1) = 0.25` and between the ground and `M` is `mu_(2) = (1)/(3)` If `M = 8 kg` then find the value of `m` so that the system will remain at rest

Options

A. `4//3 kg`
B. `8//9 kg`
C. `1 kg`
D. `8//5kg`

Answer

c

Explanation

In the free body diagram of m
`T = mg`…(1)
[No friction will act between M andm]

In the free body diagram of M
`f = mu_(2) N = 3T`…(i)
and` T + mg = N`…(ii)
From Eq (iii) `N = (m + M)g`
From Eq (ii) `mu_(2)(m + M)g = 3mg`
`m = (mu_(2)M)/((3 -mu_(2))) = (1//3 xx 8)/(( 3 - 1//3)) = 1 kg`