(a) Find the time period of a torsional pendulum whose torsional constant is K = 10π² J rad⁻¹ and moment of inertia is 10 kg m². (b) A simple pendulum of length 0.5 m hangs from the ceiling of a car accelerating horizontally at 5 m s⁻². Find its small-oscillation period.
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Question

(a) Find the time period of a torsional pendulum whose torsional constant is K = 10π² J rad⁻¹ and moment of inertia is 10 kg m². (b) A simple pendulum of length 0.5 m hangs from the ceiling of a car accelerating horizontally at 5 m s⁻². Find its small-oscillation period.

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G1 Physics · Accepted Answer

(a) T=2π√(I/K)=2π√[10/(10π²)]=2 s. (b) In the accelerating car, effective gravity magnitude is g′=√(g²+a²)=√(10²+5²)=5√5 m s⁻². Hence T=2π√(0.5/5√5)=2π/√(10√5) s, equivalent to the source result 2·5⁻¹ᐟ⁴ s. All four statements are correct.