Question

A cotton reel of mass $m$ and moment of inertia $2{\text{kgm}}^2$ is kept at rest on a smooth horizontal surface. The reel has inner radius $0.2\text{m}$ and outer radius $0.5\text{m}$. A horizontal force $F=200\text{N}$ starts acting as shown is the figure. Find the angular acceleration of the reel.

• A. $50{\text{rad/s}}^2$
• B. $20{\text{rad/s}}^2$
• C. $40{\text{rad/s}}^2$
• D. $100{\text{rad/s}}^2$

Answer 1

The correct option is B $20{\text{rad/s}}^2$

Given,
Force acting on reel, $F=200\text{N}$
Moment of inertia of reel about centre, $I=2{\text{kgm}}^2$
Radius of inner circle $r=0.2\text{m}$
Radius of outer circle $R=0.5\text{m}$

Due to force $F$, torque on the centre of the reel,
We can apply torque $e{q}^n$ about centre of mass of the reel,
$\tau =rF\sin \theta =rF\sin {90}^o$
($\theta ={90}^o$ because force is acting perpendicular to the radius)

$\tau =0.2\times 200$
$\tau =40\text{N-m}$

Also,
Torque, $\tau =I\alpha$
$\tau =I\alpha =40\text{N-m}$
$2{\text{kgm}}^2\times \alpha =40\text{N-m}$
$\alpha =20{\text{rad/s}}^2$