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If in the system is pushed by a force F as shown in Fig. (a). All surfaces are smooth except between B and C. Friction coefficient between B and C is. Minimum value of F to prevent block B from downward slipping is, all situations are same expect force is applied on block C as shown in case (b). Minimum value of F to prevent block B from downward slipping is

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$(\frac{5}{2}) μmg$

$(\frac{5}{3 μ}) mg$

$(\frac{5}{2 μ}) mg$

None of these

answer is A.

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Detailed Solution

Common acceleration, $a = \frac{F}{5 m}$

Taking A and B together as system,

$N = (2 m + m) \frac{F}{5 m} = \frac{3}{5} F$

FBD of block B

If block B is not sliding, $f = mg and f \leq μN$

$mg \leq μ \cdot \frac{3}{5} F \Rightarrow F \geq \frac{5 mg}{3 μ}$

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