MHT CET · Physics · Rotational Motion
Two bodies rotate with kinetic energies ' \(E_1\) ' and ' \(E_2\) '. Moment of inertia about their axis of rotation are ' \(I_1\) ' and ' \(I_2\) '. If \(I_1=\frac{I_2}{3}\) and \(\mathrm{E}_1=27 \mathrm{E}_2\), then the ratio of angular momenta ' \(\mathrm{L}_1\) ' to ' \(\mathrm{L}_2\) ' is
- A \(1: 3\)
- B \(3: 1\)
- C \(1: 1\)
- D \(2: 1\)
Answer & Solution
Correct Answer
(B) \(3: 1\)
Step-by-step Solution
Detailed explanation
\( \begin{aligned} & \mathrm{E}_1=\frac{1}{2} \mathrm{I}_1 \omega_1^2 \\ & \mathrm{E}_2=\frac{1}{2} \mathrm{I}_2 \omega_2^2=\frac{1}{2}\left(3 \mathrm{I}_1\right) \omega_2^2=\frac{3}{2} \mathrm{I}_1 \omega_2^2 \quad\left[\because \mathrm{I}_2=3 \mathrm{I}_1\right] \\ & \mathrm{E}_1=27 \mathrm{E}_2 \\ & \frac{1}{2} \mathrm{I}_1 \omega_1^2=\frac{81}{2} \mathrm{I}_1 \omega_2^2 \\ & \omega_1=9 \omega_2 \\ & \frac{\mathrm{L}_1}{\mathrm{~L}_2}=\frac{\mathrm{I}_1 \omega_1}{\mathrm{I}_2 \omega_2}=\frac{\mathrm{I}_1 \times 9 \omega_2}{3 \mathrm{I}_1 \times \omega_2}=3 \end{aligned} \)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A block of mass 'm', kept on a horizontal surface, is moved through a distance 's'
by applying a horizontal force (F) to it. What is the work done by the normal
reaction?MHT CET 2020 Easy - Silicon and copper are cooled from \(300 \mathrm{~K}\) to \(100 \mathrm{~K}\), the specific resistance (resistivity)MHT CET 2021 Easy
- In Young's double slit experiment with monochromatic light of wavelength 600 nm, the distance between the slits is \(10^{-3} \mathrm{~m}\). For changing the fringe width by \(3 \times 10^{-5} \mathrm{~m}\)
a) the screen is moved away from the slit by 5 cm.
b) the screen is moved 5 cm towards the slits.
c) the screen is moved 3 cm towards the slits.
d) the screen is moved away from the slits by 3 cm.MHT CET 2025 Medium - A ray of light is incident at \(60^{\circ}\) on one face of a prism of angle \(30^{\circ}\) and the emergent ray makes \(30^{\circ}\) with the incident ray. The refractive index of the prism is \(\left(\sin 30^{\circ}=0 \cdot 5, \sin 60^{\circ}=\sqrt{3} / 2\right)\)MHT CET 2024 Easy
- A particle of mass ' \(m\) ' performs uniform circular motion of radius ' \(r\) ' with linear speed ' \(v\) ' under the application of force ' \(F\) '. If \(\mathrm{m}, \mathrm{v}\) and \(\mathrm{r}\) are all increased by \(50 \%\), the necessary change in force required to maintain the particle in uniform circular motion isMHT CET 2022 Easy
- Compare the rate of loss of heat from a metal sphere at \(627^{\circ} \mathrm{C}\) with the rate of loss of heat from the same sphere at \(327^{\circ} \mathrm{C}\), if the temperature of the surrounding is \(27^{\circ} \mathrm{C}\). (nearly)MHT CET 2023 Medium
More PYQs from MHT CET
- A random variable \(x\) has the following probability distribution. Then value of \(k\) is and \(\mathrm{P}(3 \lt x \leq 6)\) has the value
MHT CET 2024 Easy - What is the SI unit of conductivity?MHT CET 2022 Medium
- Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) is differentiable function having \(f(3)=3, f^{\prime}(3)=\frac{1}{27}\) and \(\mathrm{g}(\mathrm{x})=\left\{\begin{array}{ccc}\int_3^{\mathrm{f}(x)} \frac{3 \mathrm{t}^2}{x-3} \mathrm{dt} & , & \text { if } x \neq 3 \\ \mathrm{~K} & , & \text { if } x=3\end{array}\right.\) is continuous at \(x=3\), then \(\mathrm{K}=\)MHT CET 2025 Medium
- The area bounded by the X-axis and the curve \(y=x(x-2)(x+1)\) isMHT CET 2023 Easy
- The pollen grains transferred from one flower to another in plants through biotic agency is about ________ %.MHT CET 2025 Easy
- Ratio of longest wavelength corresponding to Lyman and Balmer series in hydrogen spectrum isMHT CET 2023 Easy