Find the minimum value of force $F$ for which the system remains at rest. Take $g = 10 m / s^{2}$ .

60 N

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72 N

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80 N

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90 N

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Solution

The correct option is B $72 N$
The FBDs of the system can be shown as:

The $4 k g$ block will try to move towards right, so the frictional force $f$ will act on it towards left.

Thus, from the figure shown, we can write the equation of force as
$(a) T = 8 g$
$(b) T = F + f = F + μ (4 g)$
From the above two equations we get
$\Rightarrow 8 g = F + 0.2 \times 4 \times 10$
$\Rightarrow F = 80 - 8 = 72 N$

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