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A solid sphere of radius R is set into m...

A solid sphere of radius `R` is set into motion on a rough horizontal surface with a inear speed `v_(0)` in forward direction and an angular with a linear speed `v_(0)` in forward directioin and an angular velocity `omega_(0)=v_(0)//2R` in counter clockwise direction as shown in figure. If coefficient of friction `mu` then find
a. the time after which sphere starts pure rolling,
b. the linear speed of sphere when it starts rolling and
c. the work down by friction over a long time.

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