A string is wound around a hollow cylinder of mass 5 , kg and rad… - Vidyadip

MCQ

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 ......... $rad/s^2$ .(Neglect the mass and thickness of the string)

A
$20$
✓
$16$
C
$12$
D
$10$

✓

Answer

Correct option: B.

$16$

b
$40 + f = m\left( {R\alpha } \right)\,\,\,\,\,\,\,\,...\left( i \right)$

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

$40 - f = mR\alpha \,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)$

From $(i)$ and $(ii)$

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

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