Question

The ratio of frequencies of two oscillating pendulums is 3 : 2. Their lengths are in the ratio.

Options

• 9 : 4

• 4 : 9

• `sqrt2 : sqrt3`

• `sqrt3 : sqrt2`

Answer 1

4 : 9

Explanation:

Given, f₁ : f₂ = 3 : 2

As we know, `f = 1/(2pi)sqrt(g/l) ⇒ f ∝ 1/sqrtl`

∴ `f_1/f_2 = sqrt(l_2/l_1) ⇒ l_1/l_2 = (f_2/f_1)^2 = (2/3)^2 = 4/9`