Question

A simple pendulum has a time period of 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 `"T"_2 // "T"_1` is ______. 

Options

• 1

• `sqrt2`

• `sqrt3`

• 2

Answer 1

A simple pendulum has a time period of 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 `"T"_2 // "T"_1` is `sqrt3`

Explanation:

At height R, the value of the gravitational acceleration becomes g if it is present at the earth's surface.

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

T₁ = `2πsqrt("l"/"g")`

∴ T₂ = `2πsqrt("l"/"g"//4)`

∴ T₂ = `2 xx 2π sqrt("l"/"g"//4)`

∴ T₂ = 2T₁