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A uniform disc of mass 100 g has a diame...

A uniform disc of mass 100 g has a diameter of 10 cm. Calculate the total energy of the disc when rolling along a horizontal table with a velocity of 20 cm `s^(-1)`. (take the surface of table as reference).

Text Solution

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Given
Mass of the disc `=100g xx10^(-3) kg=(1)/(10) kg`
Velocity of dice `=20 cms^(-1)=20xx10^(-2) ms^(-1)=0.2 ms^(-1)`
`r=5 cm=5xx10^(-2)m omega=(v)/(r)=(20xx10^(-2))/(5xx10^(-2))=4`
Energy `=(1)/(2) mV^(2)+(1)/(2) I omega^(2)=(1)/(2)(mV^(2)+Iomega^(2))`, where `I=(1)/(2) mr^(2)`
`=(1)/(2)[(1)/(10)xx0.2xx0.2+(1)/(2)xx(1)/(10)xx25xx(1)/(10^(4))xx16]`
`=(1)/(2)[(4)/(1000)+(2)/(1000)]=(1)/(2)[(6)/(1000)]`
Energy `=0.005J`
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