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The system is pushed by a force F as shown in figure. All surfaces are smooth except between B and C. Friction coefficient between B and C is $μ$ . The minimum value of F to prevent block B from downward slipping

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\frac{3 mg}{2 μ}

\frac{mg}{2 μ}

\frac{5 mg}{2 μ}

answer is A.

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Detailed Solution

Horizontal acceleration of the system is

a = \frac{F}{5m}

Let N be normal reaction between B and C

Free body diagram of C gives $N = 2 ma = \frac{2}{5} F$

Now B will not slide downwards if $μ N \geq m_{B} g$

$μ (\frac{2}{5} F) \geq mg$

$F \geq \frac{5 mg}{2 μ}$

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