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# A block of mass $m=2 kg$ is resting on a rough inclined plane of inclination $30 ^{\circ}$ as shown. the coefficient of friction between the block and the plane $\mu=0.5$ . What minimum force F should be applied perpendicular to the plane on the block so that the block does not slip on the plane $(g=10 m/s^2)$

a) zero

b) 6.24 N

c) 4.34 N

d) 2.68 N

Let F be maximum force required .
Normal force $N=F+mg \cos \theta$
Since the block does not slip
$mg \sin \theta=\mu N=f$
$\qquad=\mu(F+mg \cos 30^{\circ})$
or $F=\large\frac{mg \sin 30}{\mu}$$-mg \cos 30 \qquad=\large\frac{2(10)(1/2)}{.5}$$-2(10)\bigg(\large\frac{\sqrt 3}{2}\bigg)$
$\qquad=20-17.32$
$\qquad=2.68 N$
Hence d is the correct answer

edited Jan 26, 2014 by meena.p