Question

A simple pendulum has a time period T₁ when on the earth's surface and T₂ when taken to a height R above the earth's surface, where R is the radius of the earth. The value of T₂ / T₁ is ______.

Options

• 1

• `sqrt2`

• `sqrt3`

• 2

Answer 1

A simple pendulum has a time period T₁ when on the earth's surface and T₂ when taken to a height R above the earth's surface, where R is the radius of the earth. The value of T₂ / T₁ is 2.

Explanation:

If the acceleration due to gravity is g at the surface of the earth, then · at height R, its value becomes

`"g'" = "g"(R/(R+h))^2= "g"/4`

`"T"_1=2 π sqrt(l/g)`

∴ `"T"_2= 2 π sqrt(l/(g/4)`

∴ `"T"_2=2xx2 π sqrt(l/g)`

∴ `"T"_2=2"T"_1`