Question

A cord of negligible mass is wound round the rim of fly wheel of mass 20 kg and radius 20 cm. A steady pull of 25 N is applied on the cord as shown in the figure. The fly wheel is mounted on a horizontal axle with frictionless bearings. Find the workdone by the pull when 2 m of the cord is unwound.

• A. 30 J
• B. 40 J
• C. 50 J
• D. 60 J

Answer 1

The correct option is C 50 J

Given : $M=20$ kg $R=0.2$ m $F=25$ N

Using $\tau =I\alpha$ $S=2$ m

$\therefore$ $FR=\left(M{R}^2\right)\alpha$

$⟹$ $\alpha =\frac{F}{MR}=\frac{25}{20\times 0.2}=6.25$ $rad/s^2$

Initial kinetic energy of the wheel is zero as the wheel starts at rest i.e $w_i=0$

Using $w_f^2-w_i^2=2\alpha \theta$ where $\theta =\frac{S}{R}$

$\therefore$ $w_f^2-0=2\left(6.25\right)\times \frac{2}{0.2}$ $⟹$ $w_f^2=125$ $(rad/s{)}^2$

Moment of inertia $I=M{R}^2=20(0.2{)}^2=0.8$ $kg.m^2$

From work energy theorem : $W=K.E_f-K.E_i$

$\therefore$ Work done, $W=\frac{1}{2}I{w}_f^2-0$

$⟹$ $W=\frac{1}{2}\times 0.8\times 125=50$ J