A uniform solid cylinder of mass ‘m’ & radius ‘R’ is placed on a rough horizontal table. A string attached to it passes over a pulley (disc) of mass ‘m’ & radius ‘R’ that is mounted on a smooth axle. A block is suspended at the free end of string. Cylinder rolls without slipping & there is no friction between pulley and string. System is released from rest. Find out the correct option among the following

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Acceleration of the block will be $g / 3$

Acceleration of the block will be $\frac{2 g}{5}$

Friction on the cylinder will be $\frac{m g}{5}$

Angular acceleration of pulley will $\frac{g}{3 R}$

answer is B, C.

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Detailed Solution

Pulley will not rotate as there is no friction over pulley
$B l o c k : m g - T = m a C y l i n d e r : T - f = m a f R = \frac{m R^{2}}{2} α, P u r e R o l l i n g : α = \frac{a}{R} A f t e r s o l v i n g,$
$a = \frac{2 g}{5} a n d f = \frac{m a}{2} = \frac{m g}{5}$

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