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Two blocks M and m are arranged as shown in the diagram. The coefficient of friction between the blocks is $µ_{1} = 0.25$ and between the ground and M is $µ_{2} = \frac{1}{3}$ , If M = 8 kg, then find the value of m so that the system will remain at rest.

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$8 / 5 k g$

$1 k g$

$8 / 9 k g$

$4 / 3 k g$

answer is C.

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Detailed Solution

In the free-body diagram of m [figure (a)], $T = m g$ [No friction will act between M and m]

In the free – body diagram of M [figure (b)]

$\begin{array}{l} f = μ_{2} N = 3 T \\ a n d T + M g = N \\ F r o m E q . (i i i), N = (m + M) g \\ F r o m E q . (i i) μ_{2} (m + M) g = 3 m g \\ m = \frac{μ_{2} M}{(3 - μ_{2})} = \frac{1 / 3 \times 8}{(3 - 1 / 3)} = 1 k g \end{array}$

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