Question

A solid sphere of radius 2 m and mass 20 kg is spinning with 600 rpm. How much work has to be done to stop it?

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Answer 1

When the force F is constant and the angle between the force and the displacement s is θ, then the work done is given by W = Fs cosθ. Work transfers energy from one place to another, or one form to another. The SI unit of work is the joule (J).

Answer 2

Explanation:

radius of ring , R = 0.4/2 = 0.2 m

mass of ring , M = 10 Kg

(i) moment of inertia , I = MR²

I = 10 × (0.2)² = 10 × 0.04 = 0.4 Kg.m²

(ii) angular momentum , L = Iω

∵ ω = 2πν , here I = 0.4 Kg.m² and ν = 2100rpm = 2100/60 r/s

∴ L = 0.4 × 2π × 2100/60 = 87.92 ≈ 88 Kgm²/s

(iii) Kinetic energy , K.E = 1/2Iω²

K.E = 0.4 × (2π × 2100/60)²/2

= 0.2 × 4π² × 44100/36 = 9662.408 Joule