A large solid sphere with uniformly distributed positive charge has a smooth narrow tunnel along its direction. A small particle with negative charge, initially at rest far from the sphere, approaches it along the line of the tunnel, reaches its surface with a speed `v`, and passes through the tunnel. Its speed at the centre of the sphere will be

Options

A. `0`
B. `sqrt(3) v`
C. `sqrt(2) v`
D. `sqrt(1.5) v`

Answer

4

Explanation

`V_(A) = (1)/(4 pi in_(0)) (Q)/(R ) , V_(o) = (1)/(4 pi in_(0)) .(3Q)/(2 R)`
`0 = K_(A) + (-q) V_(A) = K_(o) + (-q) V_(o)`
`(1)/(2) mv^(2) - (1)/(4 pi in_(0)) (Qq)/(R ) = (1)/(2) mv'^(2) - (1)/(4 pi in_(0)) (3Qq)/(2 R) = 0`
`(1)/(2) mv'^(2) - (3)/(2) (1)/(4 pi in_(0)) (Qq)/(R ) = 0`
`(1)/(2) mv'^(2) - (3)/(2) .(1)/(2) mv^(2) = 0`
`v' = sqrt(1.5)v`