Question

If the watch with wound spring is taken to the moon, it
A) runs faster
B) runs slower
C) does not work
D) shows no change

Answer 1

Hint
A wound spring is a part of a mechanical watch. As we know that time period is $T = 2\pi \sqrt {\dfrac{m}{k}} $, here m is the mass, k is the spring constant. As we also know that when any object is taken from earth to the moon then its gravity changes by g/6. But as in the formula of time period mass m and spring constant k both are independent of the gravity.

Complete step by step answer
The wound watch is nothing but a mechanical watch. Unlike the quartz watches that are used on a daily basis, a mechanical watch works without a battery and the circuit.
As, it is clear that the wound spring watch stores the energy in the form of spring energy and it gives kinetic energy to the rest of the parts.
As we also know that when the object goes from earth to the moon it’s gravity changes from g to g/6, where g is acceleration due to gravity. As we have to check whether this clock shows the accurate time or it runs slower or faster, for this we need to measure the time period of this watch.
As the time period of wound spring watch is proportional to the square root of the mass and inversely proportional to the square root of the spring constant i.e. $T = 2\pi \sqrt {\dfrac{m}{k}} $
Where, m is the mass of the watch
K is the spring constant.
As the value of spring constant does not depend upon the gravity because this is the material property. And we also know that mass is also independent of gravity, therefore we can say that time period is independent of gravity. Hence, we can say that the time period will remain constant.
Thus, when the watch of wound spring takes to the moon it shows no change in time.
Hence option (D) is correct.

Note
It must be noticed that the gravity on the moon surface is 1/6th times the gravity on the earth. The gravity on the moon’s surface is weaker because it is far less massive than earth. A body surface gravity is proportional to mass and inversely proportional to the square of radius. Even though you experienced the same mass on the moon as that on earth, but your weight changes.