Question

A block of mass $m$ is placed inside a smooth hollow cylinder of radius $R$ whose axis is kept horizontally. Initially system was at rest. Now cylinder is given constant acceleration $2g$ in the horizontal direction by external agent. The maximum angular displacement of the block with the vertical is:-

• A. $2{\tan }^{-1}2$
• B. ${\tan }^{-1}2$
• C. ${\tan }^{-1}1$
• D. ${\tan }^{-1}\left(\frac{1}{2}\right)$

Answer 1

The correct option is B ${\tan }^{-1}2$

Refer image,

$N\cos \theta =mg$

$N\sin \theta =mg$

$\tan \theta =2$

$\theta ={\tan }^{-1}2$