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STD 11 - 6. system of particles and rotational motion — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 6. system of particles and rotational motion4 Marks
MCQ
A rigid spherical body is spinning around an axis without any external torque. Due to change in temperature, the volume increases by $1\%$. Its angular speed 
  • A
    Will increase approximately by $1\%$
  • B
    Will decrease approximately by $1\%$
  • ✓
    Will decrease approximately by $0.67\%$
  • D
    Will decrease approximately by $0.33\%$
✓

Answer

Correct option: C.
Will decrease approximately by $0.67\%$
c
volume of spherical body, $V=\frac{4}{3} \pi R^{3}$

$\Rightarrow \frac{\Delta V}{V}=3 \frac{\Delta R}{R}$

$\Rightarrow \frac{\Delta R}{R}=0.33$

As there is no external torque angular momentum is conserved, $L=I \omega$

$\Rightarrow L=\frac{2}{5} M R^{2} \omega$

$\Rightarrow \frac{\Delta L}{L}=2 \frac{\Delta R}{R}+\frac{\Delta \omega}{\omega}$

since, $\frac{\Delta L}{L}=0$ as the magnitude is constant.

$\Rightarrow \frac{\Delta \omega}{\omega}=-2 \frac{\Delta R}{R}$

Therefore, $\omega$ decreases by $0.67 \%$

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