Q133 / 150 · MHT CET 2024 (15 May Shift 1) · Physics

If the angular velocity of a body rotating about the given axis increases by $20 \%$, then its kinetic energy of rotation will increase by

  • A
    $20 \%$
  • B
    $30 \%$
  • Correct answer
    C
    $44 \%$
  • D
    $66 \%$

Solution

$\begin{aligned} & \omega_2=\frac{120}{100} \omega_1=1.2 \omega_1 \\ & \frac{\mathrm{KE}_2}{\mathrm{KE}_1}=\frac{\frac{1}{2} \mathrm{I} \omega_2^2}{\frac{1}{2} \mathrm{I} \omega_1^2}=\frac{\omega_2^2}{\omega_1^2}=\frac{\left(1.2 \omega_1\right)^2}{\omega_1^2}=1.44 \\ \therefore \quad & \mathrm{KE}_2=1.44 \mathrm{KE}_1 \\ \therefore \quad & \left(\frac{\mathrm{KE}_2-\mathrm{KE}_1}{\mathrm{KE}_1}\right) \times 100 \\ \therefore \quad & =\left(\frac{1.44 \mathrm{KE}_1-\mathrm{KE}_1}{\mathrm{KE}_1}\right) \times 100 \\ & =0.44 \times 100=44 \%\end{aligned}$

Hence, the correct answer is option: 'C'.

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