A mass m is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release?
A
5g6
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B
g
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C
2g3
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D
g2
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Solution
The correct option is Dg2 Applying Newton's second law on hanging block mg - T = ma (i) Torque on cylinder due to tension in string about center of pulley T×R=Iα T×R=mR2α (∵I=mR2 for hollow cylinder) ⇒T=mRα (ii) As string is not slipping over pulley. a=Rα (iii) From eqns (ii) and (iii) ⇒ T = ma (iv) From eqns (i) and (iv) mg = 2ma ⇒a=g2