Q31. A solid sphere of radius 4 cm and mass 5 kg rotates about an axis through its centre with angular speed 1200 rpm. A constant opposing torque brings the sphere to rest in 10 s. What are, respectively, the magnitude of the applied torque and the number of revolutions completed before coming to rest?
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Question

Q31. A solid sphere of radius 4 cm and mass 5 kg rotates about an axis through its centre with angular speed 1200 rpm. A constant opposing torque brings the sphere to rest in 10 s. What are, respectively, the magnitude of the applied torque and the number of revolutions completed before coming to rest?

Options

G1 Physics · Accepted Answer

Initial angular speed: ω₁ = 1200 rpm = 1200×2π ÷ 60 = 40π rad·s⁻¹. Since the sphere stops in 10 s, 0 = 40π + α(10), so α = -4π rad·s⁻². For a solid sphere, I = (2 ÷ 5)MR² = (2 ÷ 5)(5)(0.04)² = 0.0032 kg·m². Torque magnitude: τ = I|α| = 0.0032×4π = 0.0128π N·m. The angular displacement during uniform angular deceleration is θ = [(ω₁+ω₂) ÷ 2]t = (40π ÷ 2)(10) = 200π rad. Number of revolutions: N = θ ÷ (2π) = 100. Correct option: D.