Question

A block comes down a stationary inclined plane of angle of inclination $\theta$ with a constant velocity. The acceleration with which the incline should be moved towards right horizontally so that the block now moves upwards with constant velocity is

• A. $gsin2\theta$
• B. $gcos2\theta$
• C. $gtan2\theta$
• D. $gcot2\theta$

Answer 1

The correct option is A

$gsin2\theta$

$mgsin\theta =\mu mgcos\theta \Rightarrow \mu =tan\theta macos\theta =mgsin\theta +\mu (mgcos\theta +masin\theta )\Rightarrow a(cos\theta +\mu sin\theta )=g(sin\theta +\mu cos\theta )a=\frac{g(sin\theta +\frac{sin\theta }{cos\theta }cos\theta )}{(cos\theta +\frac{sin\theta }{cos\theta }\times sin\theta )}=\frac{2gsin\theta cos\theta }{co{s}^2\theta +si{n}^2\theta }=gsin2\theta$