Question

A string is wrapped several times round a solid cylinder and then the end of the string is held stationary while the cylinder is released from rest with an initial motion. The acceleration of the cylinder and tension in the string will be

• A. $\frac{2g}{3}and\frac{mg}{3}$
• B. $gand\frac{mg}{2}$
• C. $\frac{g}{3}and\frac{mg}{2}$
• D. $\frac{g}{2}and\frac{mg}{3}$

Answer 1

Answer: (A)

$\frac{2g}{3}and\frac{mg}{3}$

Answer 2

Let a be the acceleration of the cylinder. Then

m g – T = ma. . . (1)

If α be the angular acceleration, then

T. R. = I α= $\left( \frac{mR^{2}}{2} \right)$α . . . (2)

As the string unwinds without slipping

a = R α . . . (3) Solving these equations, we have

a = $\frac{2}{3}gandT = \frac{mg}{3}$,