Question

A block of mass m is placed inside a smooth hollow cylinder of radius R kept horizontally. Initially system was at rest.Now cylinder is given constant acceleration 2g in the horizontal direction by external agent. The max. angular displacement of the block with the vertical is :- a. 2 tan-1 2 b. tan-1 2 c. tan-1 1 d. tan-1(1/2)

Answer 1

"ANSWER: OPTION B

According to the given data and as we know about the rotational motion the smooth hollow cylinder will have radius r and the angle for motion be alpha then the maximum angular displacement be given by the equation of rotational motion which will be

$\frac { { \mu}^{2}sin^{ 2 }\theta}{ g } =\frac { {\mu}^{ 2 }sin^{ 2 }\theta}{ 2g } \\ 2sin\theta .\quad cos\theta \quad =\quad \frac { sin^{ 2 }\theta}{ cos\quad \theta \quad} \quad =2\quad \\ tan\quad \theta \quad =\quad 2\\ \theta \quad =\quad tan^{ -1 }(2)$"