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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 the pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

Asked in JEE Main 2011 · Pulleys, strings and hanging masses

Answer: (3) 2/3g

Step-by-step solution

Body: mg-T=ma.

Pulley (a disc of the same mass m): TR=1/2mR²α, and with a=α R this gives T=1/2ma.

Substitute: mg-1/2ma=ma.

mg=3/2ma, so a=(2g)/3.

Note that R cancels completely — only the shape of the pulley matters, not its size.

Why the other options are wrong

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