JEE Physics 2023 Question with Solution

Given: Assertion A says that a pendulum clock taken to Mount Everest becomes fast. Reason R says that the value of $g$ is less at Mount Everest than on the Earth's surface.

Find: Which option correctly evaluates Assertion A and Reason R.

For a simple pendulum, the time period is

$$T \propto \sqrt{\frac{1}{g}}$$

At Mount Everest, $g$ is smaller than at the Earth's surface.

So, when $g$ decreases,

$$T \text{ increases}$$

An increase in time period means the pendulum takes more time for each oscillation, so the clock becomes slow, not fast.

Therefore, Assertion A is incorrect.

Reason R is correct because acceleration due to gravity decreases at higher altitude.

Therefore, the correct option is C.

Given: The clock is taken to a higher altitude where $g$ decreases.

Find: Whether the pendulum becomes fast or slow.

Use the relation

$$T \propto \frac{1}{\sqrt{g}}$$

So a smaller $g$ gives a larger $T$. A larger time period means fewer oscillations in the same time, so the pendulum clock runs slow.

Hence Assertion A is false, while Reason R is true. The correct option is C.