Question

A simple pendulum has length 'L₁'. When its amplitude is 'a' cm, its energy is 'E₁'. When length is 2L₁, its energy is 'E₂' Amplitude is same for both the lengths The relation between E₁ and E₂ is ______.

विकल्प

• E₂ = 4E₁

• E₂ = 2E₁

• `"E"_2 = "E"_1/2`

• E₂ = E₁

Answer 1

A simple pendulum has length 'L₁'. When its amplitude is 'a' cm, its energy is 'E₁'. When length is 2L₁, its energy is 'E₂' Amplitude is same for both the lengths The relation between E₁ and E₂ is `underline("E"_2 = "E"_1/2)`.

Explanation:

For simple pendulum T = `2pisqrt("L"/"g")`

`therefore "T"_1/"T"_2 = sqrt("L"_1/"L"_2) = sqrt(1/2)`

`because "L"_2 = 2 "L"_1`

Energy E = `1/2 "m"omega^2 "A"^2`

`therefore "E" prop omega^2 prop 1/"T"^2`

`therefore "E"_2/"E"_1 = "T"_1^2/"T"_2^2 = 1/2`

`therefore "E"_2 = "E"_1/2`