Question

A string is wound around a hollow cylinder of mass $5$kg and radius $0.5$m. If the string is now pulled with a horizontal force of $40$N, 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)

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

Answer 1

The correct option is B $16$ rad$/s^2$

$40+f=m\left(R\alpha \right)$ ..(i)

$40\times R-f\times R=m{R}^2\alpha$

$40-f=mR\alpha$ .(ii)

From (i) and (ii)

$\alpha =\frac{40}{mR}=16$.