Question

The ratio of frequencies of oscillations of two simple pendulums is 3: 4 then their lengths are in the ratio ______.

Options

• 9: 16

• 16: 9

• `sqrt(3): sqrt(4)`

• `sqrt(4): sqrt(3)`

Answer 1

The ratio of frequencies of oscillations of two simple pendulums is 3: 4 then their lengths are in the ratio 16: 9.

Explanation:

`"n"  alpha 1/sqrt(l)`

∴ `"n"_1^2  l_1 = "n"_2^2  l_2`

∴` l_1/l_2 = "n"_2^2/"n"_1^2 = (4/3)^2 = 16/9`