Question

The length of seconds pendulum is 1 m on the earth. If the mass and diameter of the planet is double that of the earth, then the length of the seconds pendulum on the planet will be

• A. 0.2 m
• B. 0.4 m
• C. 0.3 m
• D. 0.5 m

Hint:

Gravity affects the period of a pendulum. If gravity increases, the length of the pendulum decreases for the same period.

Answer 1

The Correct Option is C

Step 1: Using the formula for the length of a seconds pendulum.
The period \( T \) of a seconds pendulum is given by: \[ T = 2\pi \sqrt{\frac{L}{g}} \] Where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity. For a planet with double the mass and diameter of the earth, the gravity will be different. Step 2: Finding the new length.
Since \( g \) is proportional to the mass of the planet and inversely proportional to the square of the radius, we calculate the new gravity on the planet. For double the mass and diameter, gravity becomes half of the earth's gravity. \[ L_{\text{new}} = \frac{L_{\text{earth}}}{\sqrt{2}} = \frac{1}{\sqrt{2}} \approx 0.3 \, \text{m} \] Thus, the correct answer is (C) 0.3 m.