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More Last updated date: 01st Dec 2023
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# A rigid body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by $1\%$ . Its angular speedA. Will increase approximately by $1\%$B. Will decrease approximately by $1\%$C. Will decrease approximately by $0.67\%$D. Will increase approximately by $0.33\%$ Verified
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Hint: Here we have to first find the volume of the spherical body and then use the law of conservation of angular momentum to find what happens to the angular speed.

Complete step by step answer:The volume of a spherical body is given by
$V = \dfrac{4} {3}\pi {R^3}$
Now, the change in radius and volume will be
$\dfrac{{\Delta V}} {V} = 3\frac{{\Delta R}} {R} \\ \dfrac{{\Delta R}} {R} = 0.33\% \\$
The law of angular momentum conservation states that there is no change is angular momentum if there is no external torque acting on it.
It is given in the question that there is no external torque, so the body follows the law of angular momentum
So,
$L = I\omega$
Where $L$ is the angular momentum,
$I$ is the moment of inertia and $\omega$ is the angular velocity.

$L = \dfrac{2} {5}M{R^2}\omega \\ \dfrac{{\Delta L}} {L} = 2\dfrac{{\Delta R}} {R} + \dfrac{{\Delta \omega }} {\omega } \\$
As the magnitude remains constant, so $\dfrac{{\Delta L}} {L} = 0$
Hence,
$\dfrac{{\Delta \omega }} {\omega } = - 2\dfrac{{\Delta R}} {R} \\ = - 2 \times 0.33\% \\ = - 0.66\% \\$

Hence, option C is correct.
The angular velocity decreases by $0.66\%$ .