Question

A solid cylinder of mg 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 and hanging freely. Tension in the string required to produce angular acceleration of revolutions $s^{-2}$ is

• A. 78.5 N
• B. 157 N
• C. 25 N
• D. 50 N

Answer 1

Answer: (B)

157 N

Mass=m=50kg

Radius=0.5m

Angular acceleration$=\alpha =2rev/s^2$

Torque$=T\times R=T\times 0.5=\frac{T}{2}Nm------\left(i\right)$

We know, $T=1\alpha ------\left(ii\right)$

From (i) and (ii),

$\frac{T}{2}=1\alpha =\left(\frac{M{R}^2}{2}\right)\times (2\times 2\pi )rad/s^2$

$\therefore 1$ solid cylinder$=\frac{M{R}^2}{2}$

$\frac{T}{2}=\frac{50\times {\left(0.5\right)}^2}{2}\times 4\pi =50\pi =157N$