A hollow sphere of mass M (in kg) and radius R (in m) is rotating with an angular frequency ω (in rad/sec). It suddenly stops rotating and 75% of the K.E. is converted into heat energy. If s joule/kg-

Question

A hollow sphere of mass M (in kg) and radius R (in m) is rotating with an angular frequency ω (in rad/sec). It suddenly stops rotating and 75% of the K.E. is converted into heat energy. If s joule/kg-kelvin is the specific heat capacity of the material of the sphere, the rise of temperature of the sphere is ( J is mechanical equivalent of heat)

TestHub · Accepted Answer

Moment of inertia of a hollow sphere: I = 3 2 ​ M R 2 75% of the rotational kinetic energy becomes heat: 100 75 ​ × 2 1 ​ × 3 2 ​ M R 2 ω 2 = M s Δ T 4 1 ​ M R 2 ω 2 = M s Δ T Δ T = 4 s R 2 ω 2 ​ Here s is in J/kg-K, so no factor of J is needed.

Physics - Heat & Thermo Question with Solution | TestHub

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