A solid sphere of radius `2.45m` is rotating with an angular speed of `10 rad//s`. When this rotating sphere is placed on a rough horizontal surface then after sometime it starts pure rolling. Find the linear speed of the sphere after it starts pure rolling.

Explanation

Given, Paisson's ratio `sigma=0.2`
Longitudinal strain, `(DeltaL)/(L)=3xx10^(-3)`
`because` Poisson's ratio, `sigma=(-DeltaD//D)/(DeltaL//L)`
`impliessigma=(-DeltaR//R)/(DeltaL//L)`
`implies (DeltaR)/(R)=-sigmaxx(DeltaL)/(L)=-0.6xx10^(-3)`
`because` Volume , `V=piR^(2)L`
Therefore, percentage change in volume,
`((DeltaV)/(V)xx100)=((2DeltaR)/(R)+(DeltaL)/(L))xx100`
`=[2xx(-0.6xx10^(-3))+3xx10^(-3)]xx100`
`=0.18 %`