Question

A string is wound around a hollow cylinder of mass $5kg$ and radius $0.5m$. If the string is now pulled with a horizontal force of $40N$, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string)
Diagram

• A. $12\text{rad}/s^2$
• B. $16\text{rad}/s^2$
• C. $20\text{rad}/s^2$
• D. $10\text{rad}/s^2$

Answer 1

The correct option is B $16\text{rad}/s^2$

Diagram
Given,
Mass $m=5kg$
Radius $r=0.5kg$
Force $F=40N$
For finding acceleration,
$40+f=m\left(R\alpha \right)\dots \left(i\right)$
Torque $40\times R-f\times R=m{R}^2\alpha$
$40-f=mR\alpha \dots \left(ii\right)$
From equation $\left(i\right)$ and $\left(ii\right)$
$\alpha =\frac{40}{mR}$
$16\text{rad}/s^2$