System Of Particles And Rotational Motion Ques 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 $ $N$ ?

[2017]

(a) $0.25 $ $rad / s^{2}$

(b) $25 $ $rad / s^{2}$

(c) $5 $ $m / s^{2}$

(d) $25 $ $m / s^{2}$

Show Answer

Answer:

Correct Answer: 21.(b)

Solution:

  1. (b) Given, mass of cylinder $m=3 kg$

$R=40 cm=0.4 m$

$F=30 N ; \alpha=$ ?

As we know, torque $\tau=I \alpha$

$F \times R=MR^{2} \alpha$

$\alpha=\frac{F \times R}{MR^{2}}$

[Image]

$\alpha=\frac{30 \times(0.4)}{3 \times(0.4)^{2}} \quad$ or, $\alpha=25 $ $rad / s^{2} $

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