A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and the other hanging freely. Tension in the string required to produce an angular accel

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Solution

Q.
A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and the other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions $s^{- 2}$ is [2014]

1 25 N

2 50 N

3 78.5 N

4 157 N

Ans.
(4)

Here, mass of the cylinder, M = 50 kg

Radius of the cylinder, R = 0.5 m

Angular acceleration, $α = 2 {rev s}^{- 2}$

$= 2 \times 2 π {rad s}^{- 2} = 4 π {rad s}^{- 2}$

Torque, $τ = T R$

Moment of inertia of the solid cylinder about its axis, $I = \frac{1}{2} M R^{2}$

$∴$ $Angular acceleration of the cylinder, α = \frac{τ}{I} = \frac{T R}{\frac{1}{2} M R^{2}}$

$T = \frac{M R α}{2} = \frac{50 \times 0.5 \times 4 π}{2} = 157 N$

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