Question

Time period of oscillation of a spring is $12s$ on earth. What shall be the time period if it is taken to the moon?
A.$6s$
B.$12s$
C.$36s$
D.$72s$

Answer 1

The time period of oscillation of a spring is given by the relation $T=2\pi \sqrt{\dfrac{m}{K}}$ . Using this relation try to analyze the terms that change or different on the earth and the moon, then find the required time period of the oscillation of a spring on the moon which is some x on the earth.

Complete step by step answer:
We know that the relation to find the time period of oscillations of the spring is
$T=2\pi \sqrt{\dfrac{m}{K}}$
Where $T$ Is the time period
$m$ is the mass of the spring and
$K$ is the spring constant.
We know that mass does not change from the earth to the moon. That mass is the same on both the earth and the moon, spring constant is also the same on the earth and the moon.
Acceleration due to gravity $g$ is the only term that changes from the planet to planet that is from the earth to the moon. But in the above relation the term acceleration due to gravity is not involved and the terms that are involved in the above formula doesn’t change from the earth to the moon, all terms are the same on both the earth and the moon.
Hence the Time period of oscillation of a spring is the same on both the earth and the moon.
Given the time period of oscillation of a spring is $12s$ on earth and hence the required time period of the same on the moon is also $12s$

Hence option (B) is the correct answer.

Note:
Acceleration due to gravity $g$ is different from the earth to the moon whose value is more on earth compared to the moon. And hence the value of the weight of anything is different from the earth to the earth to the moon since the weight involves the term acceleration due to gravity.