JEE Mains · Physics · STD 11 - Gravitation
- JEE Mains 2024
- Hard
- MCQ
A simple pendulum doing small oscillations at a place \(\mathrm{R}\) height above earth surface has time period of \(T_1=4 \mathrm{~s}\). \(T_2\) would be it's time period if it is brought to a point which is at a height \(2 R\) from earth surface. Choose the correct relation. \([R=\) radius of Earth]:
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(3 \mathrm{~T}_1=2 \mathrm{~T}_2\)
Step-by-step Solution
Detailed explanation
\(\mathrm{T}_1=2 \pi \sqrt{\frac{\ell}{\mathrm{GM}}(2 \mathrm{R})^2}\)
\(\mathrm{~T}_2=2 \pi \sqrt{\frac{\ell}{\mathrm{GM}}(3 \mathrm{R})^2}\)
\(\therefore \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{2}{3}\)
More questions from Physics
- A metal surface is illuminated by a radiation of wavelength \(4500 \; \mathring A\). The ejected photo-electron enters a constant magnetic field of \(2 \; mT\) making an angle of \(90^{\circ}\) with the magnetic field. If it starts revolving in a circular path of radius \(2 \; mm\), the work function of the metal is approximately ............. \(eV\)JEE Mains 2022 Hard
- An electron in the ground state of the hydrogen atom has the orbital radius of \(5.3 \times 10^{-11} \mathrm{~m}\) while that for the electron in third excited state is \(8.48 \times 10^{-10} \mathrm{~m}\). The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is _______.JEE Mains 2025 Easy
- A projectile is thrown upward at an angle \( 60^{\circ} \) with the horizontal. The speed of the projectile is 20 m/s when its direction of motion is \( 45^{\circ} \) with the horizontal. The initial speed of the projectile is __________ in m/s.JEE Mains 2026 Easy
- A \(1\) kg block subjected to two simultaneous forces \((2\hat{i} + 3\hat{j} + 4\hat{k})\) N and \((3\hat{i} - \hat{j} - 2\hat{k})\) N is moved a distance of \(25\) m along \((3\hat{i} - 4\hat{j})\) direction. The work done in this process is _____ J.JEE Mains 2026 Medium
- If we need a magnification of \(375\) from a compound microscope of tube length \(150\; \mathrm{mm}\) and an objective of focal length \(5\; \mathrm{mm}\), the focal length of the eye-piece, should be close to.....\(mm\)JEE Mains 2020 Medium
- The charge accumulated on the capacitor connected in the following circuit is________ \(\mu \mathrm{C}\) (Given \(\mathrm{C}=150\ \mu \mathrm{F}\))
JEE Mains 2024 Hard
More PYQs from JEE Mains
- A plane electromagnetic wave, has frequency of \(2.0 \times 10^{10}\, Hz\) and its energy density is \(1.02 \times 10^{-8}\, J / m ^{3}\) in vacuum. The amplitude of the magnetic field of the wave is close to\(....nT\) \(\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{\circ} \frac{ Nm ^{2}}{ C ^{2}}\right.\) and speed of \(1 ight\) \(\left.=3 \times 10^{8}\, ms ^{-1}\right)\)JEE Mains 2020 Hard
- In a large building, there are \(15\) bulbs of \(40\ W\), \(5\) bulbs of \(100\ W, 5\) fans of \(80\ W\) and \(1\) heater of \(1\ kW\). The voltage of electric mains is \(220\ V\). The minimum capacity of the main fuse of the building will be ................ \(A\)JEE Mains 2014 Medium
- The boxes of masses \(2\, {kg}\) and \(8\, {kg}\) are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass \(8\; {kg}\) to strike the ground starting from rest. (use \(\left.{g}=10\, {m} / {s}^{2}\right)\) (in \({s}\))
JEE Mains 2021 Hard