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

Answer: (B)

$16 \; rad/s^2$

Answer 2

$40 + f = m(R \alpha)$ .....(i)
$40 \times R - f \times R = mR^2 \alpha$
$40 - f = mR \alpha$ ...... (ii)
From (i) and (ii)
$\alpha = \frac{40}{mR} = 16$