System of Particles and Rotational Motion - Result Question 21
21. A rope is wound around a hollow cylinder of mass $3 kg$ and radius $40 cm$. What is the angular acceleration of the cylinder if the rope is pulled with a force of $30 N$ ?
(a) $0.25 rad / s^{2}$
(b) $25 rad / s^{2}$
(c) $5 m / s^{2}$
(d) $25 m / s^{2}$
[2017]
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Answer:
Correct Answer: 21. (b)
Solution:
- (b) Given, mass of cylinder $m=3 kg$
$R=40 cm=0.4 m$
$F=30 N ; \alpha=$ ?
As we know, torque $\tau=I \alpha$
$F \times R=MR^{2} \alpha$
$\alpha=\frac{F \times R}{MR^{2}}$
$\alpha=\frac{30 \times(0.4)}{3 \times(0.4)^{2}} \quad$ or, $\alpha=25 rad / s^{2} \quad F=30 N$
