SATHEE: System of Particles and Rotational Motion

System of Particles and Rotational Motion - Result Question 28

28. A solid cylinder of mass $50 k g$ 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 :

(a) $25 N$

(b) $50 N$

(c) $78.5 N$

(d) $157 N$

[2014]

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Answer:

Correct Answer: 28. (d)

Solution:

(d) Here $α = 2$ revolutions $/ s^{2} = 4 π r a d / s^{2}$ (given)

$I_{cylinder} = \frac{1}{2} M R^{2} = \frac{1}{2} (50) (0.5)^{2} = \frac{25}{4} K g - m^{2}$

As $τ = I α$ so $T R = I α$

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

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System of Particles and Rotational Motion - Result Question 28

28. A solid cylinder of mass 50kg 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 :

Answer:

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28. A solid cylinder of mass $50 k g$ 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 :