The mass and the diameter of a planet are three times the respective values for the earth

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 $2 \mathrm{~s}$. The period of oscillation of the same pendulum on the planet would be:

  1. $\frac{\sqrt{3}}{2} s$

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

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

  4. $2 \sqrt{3} \mathrm{~s}$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Oscillations chapter.

JEE Main Previous Year 11 Jan 2019, II

Correct Option: 4

Solution:

The mass and the diameter of a planet are three times the respective values for the earth

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Free

90 Qs. 360 Marks 180 Mins

Concept:

A simple pendulum is one which can be considered to be a point mass suspended from a string or rod of negligible mass. It is a resonant system with a single resonant frequency. For small amplitudes, the period of such a pendulum can be approximated by

Calculation:

Period of motion of a pendulum is given by

 ----(1)

On the surface of earth, let period of motion is Te and acceleration due to gravity is ge

 ----(2)

On another planet, let period of motion is TP and gravitational acceleration is gp

 ----(3)

(∴ Pendulum is same, so l will be same)

From Equations (2) and (3),

 ----(4)

Now, 

and 

Given, Mp = 3Me

and Rp = 3Re

 ----(5)

From Equations. (4) and (5) 

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