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)

Options

A. 2.1 R
B. 2.3 R
C. 2.7 R
D. 2.5 R

Answer

C

Explanation

At the topmost point of the loop minimum value of linear speed of centre of sphere should b:
`v=sqrt(gR)` or translational kinetic energy `=K_(T) = 1/2 mv^(2) = 1/2 mgR`
In Case of pure rolling of a solid the ratio of rational to translational kinetic energy is
`K_(R)/K_(T) = 2/5` `therefore` Total kinetic energy at topmost point should be
`therefore K = (5+2)/5, K_(T) = 7/5 (1/2 mgR) = 7/10 mgR`
Now from conservation of mechanical energy: `7/10 mgR = mg(h-2R) therefore h=2,7 R`