First slide

Friction on inclined plane of angle more than angle of repose

Question

An object is kept on a smooth inclined plane of 1 in l. The horizontal acceleration to be imparted to the inclined plane so that the object is stationary relative to the incline is given by

Moderate

A

$g \sqrt{(l^{2} - 1)}$
B

$g (l^{2} - 1)$
C

$g / \sqrt{(l^{2} - 1)}$
D

$g / (l^{2} - 1)$

Solution

See fig.
From figure
$\tan θ = 1 / \sqrt{(l^{2} - 1)}$
A horizontal acceleration imparted to the inclined plane has a component $acos θ$ down the plane.
The object will appear stationary relative to the incline if
$acos θ = gsin θ$
$a = gtan θ = g / \sqrt{l^{2} - 1}$ .

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