Flux passing through the shaded surface of a sphere when a point charge q is placed at the center is (radius of the sphere is R)

Explanation

K.E = K.E of sphere due to rolling + K.E due to rotation about 0
`=[(1//2)mv^(2) +1//2 Iomega^(2)] + 1/2 I xx v^(2)//R^(2) = (7//10)mv^(2) + 1/2 xx 2/5 mr^(2) xx v^(2)//R^(2) =(7//10) mv^(2) [1+(2r^(2))/(7R^(2))]`