Question:
A body of mass $ 5 \,kg $ acquires an angular acceleration of $ 10\, rad\, s^{-2} $ by an applied torque of $ 2 \,N m $ . Find its radius of gyration.
A body of mass $ 5 \,kg $ acquires an angular acceleration of $ 10\, rad\, s^{-2} $ by an applied torque of $ 2 \,N m $ . Find its radius of gyration.
Updated On: Jun 14, 2022
- $ 2.5\,m $
- $ \sqrt{2.5} \,m $
- $ \sqrt{0.2}\, m $
- $ 0.2\,m $
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The Correct Option is D
Solution and Explanation
$m=5\,Kg$,
$\alpha=10$ rad $s^{-2}$,
$\tau=2\,N\,m$
Torque, $\tau=I \alpha=mk^{2}\alpha \left(\because I=mk^{2}\right)$
where $k$ is the radius of gyration
$\therefore 2=5\times k^{2}\times10$
or $k^{2}=0.04$ or $k=0.2\,m$
$\alpha=10$ rad $s^{-2}$,
$\tau=2\,N\,m$
Torque, $\tau=I \alpha=mk^{2}\alpha \left(\because I=mk^{2}\right)$
where $k$ is the radius of gyration
$\therefore 2=5\times k^{2}\times10$
or $k^{2}=0.04$ or $k=0.2\,m$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
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- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.