The radius of gyration of a compound pendulum about the

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The radius of gyration of a compound pendulum about the point of suspension is 100 mm. The distance between the point of suspension and the centre of mass is 250 mm. Considering the acceleration due to gravity is 9.81 m/s², the natural frequency (in radian/s) of the compound pendulum is _________.

1. 5.660 rad / sec
2. 10.660 rad / sec
3. 15.660 rad / sec
4. 115.660 rad / sec

Correct Option: C

For compound pendulum,

θ̇̇ +		mg	a		θ = 0
		l

∵ I mk² = m(0.1)²
I = m(0.01) kg m²
a = 0.250 m
g = 9.81 m/s²

θ̇̇ +		m × 9.81 × 0.250		= 0
		(0.01)m

ω_n = √245.25 = 15.660 rad / sec