Question

A person wearing a wrist watch that keeps the correct time at the equator goes to N-pole. His watch will
A. keep correct time
B. gain time
C. loose time
D. cannot say

Answer 1

Use the formula for the time period of oscillation of a spring. This formula gives the relation between the time period of the spring, mass of the oscillating body and the spring constant. Check the effect of change in acceleration due to gravity on the time period of the wrist watch.

Formula used:
The time period $T$ of a spring is given by
$T = 2\pi \sqrt {\dfrac{m}{k}}$ …… (1)
Here, $m$ is the mass of the oscillating object and $k$ is the spring constant.

Complete step by step answer:
We have given that a person wearing a wrist watch that keeps correct time at the equator goes to the North pole.We know that when a person walks from the equator to the South or North Pole. The value of acceleration due to gravity on the surface of the Earth changes. This change occurs because the radius of the Earth from the centre of the Earth is not constant as the shape of the Earth is not perfectly spherical.The value of acceleration due to gravity affects may physical quantities.Many of the wrist watches consist of a spring and this spring determines the time period of the wrist watch. The time shown by the wrist watch will change when the person goes to the North pole from the equator if there is any effect of acceleration due to gravity on the time period of the spring and hence, the wrist watch.
Rewrite equation (1) for the time period of the spring.
$T = 2\pi \sqrt {\dfrac{m}{k}}$
From the above equation, it can be concluded that the time period of a spring depends only on the mass of the oscillating body and the spring constant and not on the acceleration due to gravity.The mass oscillating with the spring in the wrist watch and the spring constant of the spring remains the same anywhere on the Earth.

Therefore, the watch keeps correct time at the North Pole.Hence, the correct option is A.

Note: One can also solve the same question by a very simple method instead of considering the time period of the spring in the watch. One can directly conclude that the time period of a watch does not depend on the acceleration due to gravity at that North Pole on the surface of the Earth. Hence, the time shown by the watch will be the same.