A uniform solid brass sphere is rotating with angular speed ω$$0$$ about a diameter. If its temperature is now increased by $$100$$°C, what will be its new angular speed. (Given$$ αB $$=$$ $$2.0$$ × $$10-5$$ per °$$C)

Question

A uniform solid brass sphere is rotating with angular speed ω$$0$$ about a diameter. If its temperature is now in­creased by $$100$$°C, what will be its new angular speed. (Given$$ αB $$=$$ $$2.0$$ × $$10-5$$ per °$$C)

Infinity Learn · Accepted Answer

Due to increase in temperature, radius of the sphere changes.            Let $$R0and$$ $$R100$$ be radius of sphere at $$0$$°C and $$100$$°C, respectively.$$R100=$$ $$R0(1$$ $$+$$α× $$100)Squaring$$ both the sides and neglecting higher terms⇒$$R1002=R02(1+2$$α×$$100)By$$ the law of conservation of angular momentum⇒$$25MR02$$ω$$1=25MR1002$$ω$$2$$,$$R02$$ω$$1=R02(1+2$$×$$2$$×$$10$$−$$5$$×$$100)$$ω$$2$$ω$$2=$$ω$$1(1+4$$×$$10$$−$$3)=$$ω$$01.004=0.996$$ω$$0$$

A uniform solid brass sphere is rotating with angular speed $ω_{0}$ about a diameter. If its temperature is now increased by 100°C, what will be its new angular speed. (Given $α_{B}$ = 2.0 × $10^{- 5}$ per °C)

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A uniform solid brass sphere is rotating with angular speed ω0 about a diameter. If its temperature is now in­creased by 100°C, what will be its new angular speed. (Given αB = 2.0 × 10-5 per °C)

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Ready to Test Your Skills?

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A uniform solid brass sphere is rotating with angular speed $ω_{0}$ about a diameter. If its temperature is now increased by 100°C, what will be its new angular speed. (Given $α_{B}$ = 2.0 × $10^{- 5}$ per °C)