First slide

Friction on inclined plane of angle more than angle of repose

Question

A body is projected up a 45⁰ rough incline. If the coefficient of friction is 0.5, then the retardation of the block is

Moderate

A

$\frac{g}{2 \sqrt{2}}$
B

$\frac{g}{\sqrt{2}}$
C

$\frac{3 g}{2 \sqrt{2}}$
D

$\frac{g}{2}$

Solution

Acceleration, $a = (g \sin θ + μ g \cos θ)$
$= (g \sin 45 ° + 0.5 \times g \times \cos 45 °)$
$= \frac{g}{\sqrt{2}} + 0.5 \times g \times \frac{1}{\sqrt{2}} = \frac{3 g}{2 \sqrt{2}}$

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