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A solid sphere of diameter 2 cm and of m...

A solid sphere of diameter 2 cm and of mass 20 g is rolling with a velocity of 3 cm.`s^(-1)`. What is the total kinetic energy of the sphere?

Text Solution

Verified by Experts

Let M = mass of the sphere , R = radius of the sphere V = linear velocity of the sphere `I= (1)/(5) "MR"^(2)` (moment of inertia of the sphere about its diameter ), `omega= (V)/( R)`
Total kinetic energy of the sphere
= translational kinetic energy + rotational kinetic energy
`=(1)/(2)"MV"^(2)+(1)/(2)Iomega^(2)=(1)/(2)"MV"^(2)+(1)/(2)xx(2)/(5)"MR"^(2)((V)/(R))^(2)`
`=(1)/(2)"MV"^(2)+(1)/(5)"MV"^(2)=(7)/(10)"MV"^(2)=(7)/(10)xx20xx(3)^(2)`
= 126 erg.
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