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A system of two blocks of masses $m = 2 k g$ and $M = 8 k g$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M so that the blocks move together will be:

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$49 N$

$9.8 N$

$39.2 N$

$78.4 N$

answer is C.

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Detailed Solution

Clearly, from (i) $' a'$ will be maximum when $f = f_{\lim}$
So, $a_{\max} = \frac{f_{l i m}}{2} = \frac{μ \times 2 g}{2} = μ g$
From (ii), $F_{\max} = 8 a_{\max} + f_{\lim} = 8 μ g + 2 μ g = 10 μ g = 49 N$

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