System of Particles and Rotational Motion - Result Question 28

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28. A solid cylinder of mass $50 kg$ and radius 0.5 $m$ is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions $s^{-2}$ is :

======= ####28. A solid cylinder of mass $50 kg$ and radius 0.5 $m$ is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions $s^{-2}$ is :

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/system-of-particles-and-rotational-motion/system-of-particles-and-rotational-motion—result-question-28.md (a) $25 N$

(b) $50 N$

(c) $78.5 N$

(d) $157 N$

[2014]

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Answer:

Correct Answer: 28. (d)

Solution:

  1. (d) Here $\alpha=2$ revolutions $/ s^{2}=4 \pi rad / s^{2}$ (given)

$I _{\text{cylinder }}=\frac{1}{2} MR^{2}=\frac{1}{2}(50)(0.5)^{2}=\frac{25}{4} Kg-m^{2}$

As $\tau=I \alpha \quad$ so $TR=I \alpha$

$\Rightarrow T=\frac{I \alpha}{R}=\frac{(\frac{25}{4})(4 \pi)}{(0.5)} N=50 \pi N=157 N$