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JEE Main 2004 (AIEEE) · Friction on an Incline

Friction on an Incline question from JEE Main 2004 (AIEEE)

Q31JEE Main 2004 · AIEEEEasy

Friction on an Incline

A block rests on a rough inclined plane making an angle of $30^\circ$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictional force on the block is $10\text{ N},$ the mass of the block (in $\text{kg}$ ) is $(\text{take } g = 10\text{ m/s}^{2})$

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Answer: (c)

Block at rest: static friction equals the component of weight along the incline.
$f = mg\sin 30^\circ \Rightarrow 10 = m(10)(0.5)$
$m = 2\text{ kg}$ (check: $\mu_s\cos 30^\circ = 0.69 > \sin 30^\circ$ , so it can stay at rest).
So the answer is (c) 2.0.

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