Question

A wheel (disc) of radius $10cm$ can rotate freely about its centre as shown in figure. $A$ string is wrapped over its rim and is pulled by a force of $5N$. it is found that the torque produces an angular acceleration $20rad/s^2$ in the wheel. calculate the mass of the wheel.

• A. $25kg$
• B. $50kg$
• C. $75kg$
• D. $10kg$

Answer 1

The correct option is A $25kg$

The force acting on the wheel are $\left(2\right)$ $W$ dur to gravity $,\left(2\right)N$ due to the support at the centre and $\left(3\right)$ $F$ due to tension $.$

the torque of W and N are separately zero and that of $F$ is $F.r$ The net torque is

Torque $=\left(F\right).\left(r\right)$

$T=\left(5.0N\right)\left(10cn\right)=0.50N-m$

The moment of inertia$;44

$=$ Torque $/$angular acceleration

$=0.50/2=0.24kg-m²=\approx 25kg$

Hence,

option $\left(A\right)$ is correct answer.