An insulated chamber at a height `h` above the earth's surface and maintained at `30^(@)C` has a clock fitted with an uncompensated pendulum. The maker of the clock for the chamber mistakenly design it to maintain correct time at `20^(@)C` at that height. it is found that if the chamber were brought to earth's surface the clock in it would click correct time at `30^(@)C`. the coefficient of linear expansion of the material of pendulum is (earth's radius is R)

Options

A. `(trianglel)/(10l)`
B. `(5R)/(h)`
C. `(h)/(5R)`
D. `(h)/(20R)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Problem
We have a pendulum clock in an insulated chamber at a height \( h \) above the Earth's surface, maintained at \( 30^\circ C \). The clock was designed to keep correct time at \( 20^\circ C \). When brought to the surface, it keeps correct time at \( 30^\circ C \). We need to find the coefficient of linear expansion \( \alpha \) of the pendulum material.

### Step 2: Write the Time Period of the Pendulum
The time period \( T \) of a simple pendulum is given by the formula:
\[
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