A drop of water of mass m falls away from the bottom of charged conducting sphere of radius R, carrying with it a charge `q_(1)` and leaving the sphere a uniformly distributed charge `q_(2)`. The kinetic energy of the drop after it has fallen height h is -

Options

A. `(1)/(4pixi_(0))q_(1)q_(2)((h)/(R(R+h)))`
B. mgh
C. `(1)/(4pixi_(0))q_(1)q_(2)((h)/(R(R+h)))+mgh`
D. `(1)/(4pixi_(0))(q_(1)q_(2))/(h)+mgh`

Answer

C

Explanation

`U_(i)+K_(i)=U_(f)+K_(f)`
`(Kq_(1)q_(2))/(R)=-mgh+(Kq_(1)q_(2))/(R+h)+K_(f)`
`(Kq_(1)q_(2))/(R)-(Kq_(1)q_(2))/(R+h)+mgh=K_(f)`