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A solid cylinder of mass M and R is mounted on a frictionless horizontal axle so that it can freely rotate about this axis. A string of negligible mass is wrapped round the cylinder and a body of mass m is hung from the string as shown in figure the mass is released from rest then___

The acceleration with which the mass falls is

(A) g 

(B) (mg / M) 

(C) [mg / (M + m)] 

(D) [(2mg) / (M + 2m)]

1 Answer

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Best answer

Correct option: (D) [(2mg) / (M + 2m)]

Explanation:

When a point mass is connect string which is wound round solid body.

then when mass is released,

acceleration of point mass = a = [g / {1 + (I / mR2)}]

here I = [(MR2) / α]–– for solid cylinder,

hence

a = [g / {1 + {{(MR2) / 2} / (mR2)}}]

= [g / {1 + {1 / (2m)}}]

= [(2mg) / (M + 2m)]

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