Question

If the length of an oscillating simple pendulum is made `1/3` times at a place keeping amplitude the same, then its total energy (E) will be ______ 

Options

• 2E

• 6E

• 4E

• 3E

Answer 1

If the length of an oscillating simple pendulum is made `1/3` times at a place keeping amplitude the same, then its total energy (E) will be 3E.

Explanation:

`T = 2pisqrt(ℓ/g)`

`(2pi)/omega = 2pisqrt(ℓ/g)`

`omega = sqrt(g/ℓ)` 

∴ `omega ∝ 1/sqrtℓ`

∴ `omega_2/omega_1 = sqrt(ℓ_1/ℓ_2) = sqrt((ℓ_1)/(ℓ_1"/"3)) = sqrt3`

∴ `omega_2 = sqrt3 omega_1`

Now E ∝ ω²

∴ `E_2/E_1 = (omega_2^2)/(omega_1^2) = 3`

∴ E₂ = 3E₁