Question

A certain simple pendulum has a period on earth of 1.72 s.

What is its period on the surface of Mars,where the acceleration due to gravity is 3.71 m/s² ?

Answer 1

Concepts and reason

The concept required to solve the given problem is period of a pendulum.

Initially, write the expression for period of the pendulum in terms of length and acceleration due to gravity. Then, obtain the relation between the period and acceleration due to gravity on earth and mars. Finally, calculate the period on mars by using this relation.

Fundamentals

The period of a pendulum is depends on acceleration due to gravity and length of the pendulum. The mathematical expression for period T of a pendulum is given by following expression.

Here, l is the length of the pendulum, and g is the acceleration due to gravity.

The period of the pendulum is different is not same on all the planets because it is depends on the acceleration due to gravity.

The expression for period T of the pendulum is,

The relation between period and acceleration due to gravity on earth and mars is given by following expression.

Here, is the period on earth, is the acceleration due to gravity on earth, is the period on mars, and is the acceleration due to gravity on mars.

The relation between period and acceleration due to gravity on earth and mars is given by following expression.

Rearrange the above equation for period on the mars.

Substitute 1.72 s for for and for in the above equation.

Ans:

The period on mars is 2.79 s.