JEE Mains · Physics · STD 11 - System of particles and rotational motion
- JEE Mains 2024
- Hard
- Numerical
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _______ hours \(30\) minutes.
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(13\)
Step-by-step Solution
Detailed explanation
By conservation of angular momentum
\(\mathrm{I}_1 \omega_1=\mathrm{I}_2 \omega_2\)
\(\left(\frac{2}{5} \mathrm{MR}^2\right) \frac{2 \pi}{\mathrm{T}_1}=\frac{2}{5} \mathrm{M}\left(\frac{3}{4} \mathrm{R}\right)^2 \frac{2 \pi}{\mathrm{T}_2}\)
\(\frac{1}{\mathrm{~T}_1}=\frac{9}{16 \mathrm{~T}_2}\)
\(\frac{1}{\mathrm{~T}_2}=\frac{9}{16} \times \mathrm{T}_1=\frac{9}{16} \times 24 \mathrm{hr}=\frac{27}{2} \mathrm{hr}=13 \mathrm{hr} 30 \text { mins. }\)
More questions from Physics
- If \(2\) mole of an ideal monoatomic gas at temperature \(T\), is mixed with \(6\) mole of another ideal monoatomic gas at temperature \(2T\) then the temperature of mixture is :JEE Mains 2026 Medium
- How many alpha and beta particles are emitted when Uranium \({ }_{92} U ^{238}\) decays to lead \({ }_{82} Pb ^{206}\) ?JEE Mains 2022 Medium
- Given below are two statements: Statement \(I:\) If heat is added to a system, its temperature must increase. Statement \(II:\) If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given belowJEE Mains 2023 Medium
- A body of mass \(2 \mathrm{~kg}\) begins to move under the action of a time dependent force given by \(\overrightarrow{\mathrm{F}}=\left(6 \mathrm{t} \hat{\mathrm{i}}+6 \mathrm{t}^2 \hat{\mathrm{j}}\right) \mathrm{N}\). The Power developed by the force at the time \(t\) is given by _______.JEE Mains 2024 Hard
- A thin ring of \(10\, cm\) radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of \(40\,\pi \,rad\,{s^{ - 1}}\) about its axis, perpendicular to its plane. If the magnetic field at its centre is \(3.8 \times {10^{ - 9}}\,T\), then the charge carried by the ring is close to \(\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,N/{A^2}} \right)\)JEE Mains 2019 Medium
- A sportsman runs around a circular track of radius \(r\) such that he traverses the path \(A B A B\). The distance travelled and displacement, respectively, are
JEE Mains 2025 Medium