The mass and the diameter of a...|Gravitation|JEEMAIN 2019

JEE MAIN 2019

11-01-2019 S2

Question

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2s. The period of oscillation of the same pendulum on the planet would be:

Select the correct option:

$\frac{2}{\sqrt{3}} \mathrm{~s}$

$\frac{3}{2} \mathrm{~s}$

$\frac{\sqrt{3}}{2} \mathrm{~s}$

$2 \sqrt{3} s$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$$T = 2\pi\sqrt{\frac{\ell}{g}} \implies \frac{T_1}{T_2} = \sqrt{\frac{g_2}{g_1}}$$$$T_2 = 2 \sqrt{\frac{g_1}{g_2}}$$$$g_2 = \frac{3GM}{(3R)^2} = \frac{g}{3}$$$$T_2 = 2\sqrt{3} \text{ s}$$

Question Tags

JEE Main

Physics

Hard

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