Question

A system of smooth hollow cylinder and block was initially at rest as shown. If cylinder is given constant acceleration 2g in horizontal direction, then the maximum angular displacement of the block with the vertical is:

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

Answer 1

The correct option is A $2ta{n}^{-1}\left(2\right)$


Apply W.E. theorem in the frame of hollow cylinder:
$2mgRsin\theta mgR(1-cos\theta )=0$
$\Rightarrow 2sin\theta =1-cos\theta$
$\Rightarrow \theta =2ta{n}^{-1}\left(2\right)$