QJEEM11Ph2c76: JEE Main 2011 Physics - Class 11 JEEM11Ph2c76 Solution: A mass hangs with the help of a string wrapped around a pulley…

Question

Verified Solution • 2025–26 Session moderate

A mass

m

hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass

m

and radius

R.

Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass

m,

if the string does not slip on the pulley, is:

Accepted Answer

This is the free body diagram of pulley and mass AIEEE 2011 Physics - Rotational Motion Question 206 English Explanation

For translation motion of the block,

mg - T = ma\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,.....\left( 1 \right)

For rotational motion of the pulley,

T\times R = I\alpha = I{a \over R}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( 2 \right)

where

\alpha =

angular acceleration of disc =

{a \over R}

and

I = {1 \over 2}m{R^2}

(For circular disc)

Solving

(1)

&

(2),

a = {{mg} \over {\left( {m + {I \over {{R^2}}}} \right)}} = {{mg} \over {m + {{m{R^2}} \over {2{R^2}}}}}

= {{2mg} \over {3m}} = {{2g} \over 3}

Step-by-Step Verified Solution