Question

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

• A. 0.5 m
• B. 1 m
• C. 1.5 m
• D. 2 m

Hint:

The length of the seconds pendulum is inversely proportional to the square root of the acceleration due to gravity on the planet.

Answer 1

The Correct Option is D

Step 1: Relation between Length and Acceleration due to Gravity.
The length \( L \) of a seconds pendulum is related to the acceleration due to gravity \( g \) by: \[ L = \frac{g T^2}{4 \pi^2} \] where \( T \) is the time period of the pendulum. The time period of the pendulum depends on the gravitational acceleration, and for a planet with half the mass and diameter of the Earth, the value of \( g \) would be proportional to the inverse of the square of the radius. Thus, the length of the seconds pendulum on the planet will be twice the length on Earth, as \( g \) is halved.
Step 2: Final Answer.
Thus, the length of the seconds pendulum on the planet is 2 m.