First slide

Friction on horizontal surface

Question

A horizontal force F acts on the block of mass m and the block remains stationary, the minimum force F required to pull it( $μ$ = $\frac{1}{2}$ ) is:

Moderate

A

$\frac{mg}{2}$
B

$\frac{mg}{2} \cos θ$
C

$\frac{mg}{\sqrt{5}}$
D

none of these

Solution

For minimum force the object should be pulled at angle equal to angle of friction and applied force should be equal to
$\Rightarrow \tan θ = μ = \frac{1}{2}$
hence $\cos θ = \frac{2}{\sqrt{5}} and \sin θ = \frac{1}{\sqrt{5}}$
Hence applied force F = $\frac{mg}{\sqrt{5}}$

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