Question

A 25kg uniform solid sphere with a 20cm radius is suspended by a vertical wire such that the point of suspension

Answer 1

Hello dear,

● Answer- 4π s.

● Explaination-
# Given-
m = 25 kg
r = 20 cm = 0.2 m
θ = 1 rad
τ = 0.1 Nm

# Solution-
Moment of inertia of solid sphere is-
I = 2mr^2/5
I = 2 × 25 × (0.2)^2 / 5
I = 0.4 kgm^2

Also torque is given by-
τ = -kθ
k = -τ/θ
k = -0.1 / 1
k = 0.1 Nm/rad

Period of oscillation is given by-
T = 2π√(I/k)
T = 2π √(0.4/0.1)
T = 4π s

Period of oscillation will be 4π s.

Hope this helps you...