# 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 : Option 1) 25 N Option 2) 50 N Option 3) 78.5 N Option 4) 157 N

As learnt in @7077

$m=50kg, r=0.5m$

$\alpha =2 rev/s^{2}$

Torque by Tension in string

$T\times R= T\times 0.5=\frac{T}{2} N-M$

$T=I\alpha \Rightarrow \frac{T}{2}=I\alpha$

$\Rightarrow \frac{T}{2}=\left ( \frac{MR^{2}}{2} \right )\times (2\times 2\pi )$

$\frac{T}{2}=\frac{50\times (0.5)^{2}\times 4\pi }{2}$

$T=157N$

Option 1)

25 N

This solution is incorrect.

Option 2)

50 N

This solution is incorrect.

Option 3)

78.5 N

This solution is incorrect.

Option 4)

157 N

This solution is correct.

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