AA solid sphere lying on a Smooth horizontal surface is pulled by a force acting on its top most point - Physics - System Of Particles And Rotational Motion

Question

AA solid sphere lying on a Smooth horizontal surface is pulled
by a force acting on its top most point what will be the distance
travelled by the sphere during the time it makes one complete
revolution ?

Jyoti Pant · Accepted Answer

Suppose the radius of sphere is 'R'
 and the force by which it is pulled is 'F'
Now, torqueτ=R×Fand τ=I×αSo, angular acceleration,α=τI=R×F23mR2=3F2mRSince α is constant, we haveangular displacement, θ=12αt2=2πor t2=4παAlso we have s=ut+12at2=0+12at2=12×Fm×4πα=12×Fm×4π×2mR3F=4πR3

AA solid sphere lying on a Smooth horizontal surface is pulled by a force acting on its top most point. what will be the distance travelled by the sphere during the time it makes one complete revolution ?