The system of two blocks is at rest as shown in the figure. A variable horizontal force is applied to the upper block. The maximum possible contact force exerted by the horizontal ground surface on the lower block is (coefficient of friction for both the contacts is $μ$ )

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TestHub · Accepted Answer

The lower block will not move in this case Apply equilibrium equation on upper block

$\Rightarrow F = μ mg$

Total normal force = $3 m g$

maximum friction force on lower black by ground $= μ N$

$= 3 μ m g$

$\Rightarrow$ Resultant force $= \sqrt{{(μ N)}^{2} + N^{2}}$

$= mg \sqrt{9 μ^{2} + 9}$

$= 3 m g \sqrt{1 + μ^{2}}$

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