Question

A pendulum clock which keeps correct time at the surface of the earth is taken into a mine, then

• A. it keeps correct time
• B. it gains time
• C. it loses time
• D. none of these

Answer 1

The correct option is C it loses time

Time period of a pendulum is given by:
$T=2\pi \sqrt{\frac{L}{g}}$
When the pendulum is taken into a mine, we are going towards earth's centre.
As we go deep, the value of gravity decreases as:
$g^{\prime }=g(1-\frac{d}{R})$
So g decreases, the values of time period increases.
Implies, the pendulum takes more time to complete one full swing. Hence the clock loses time.