Question

A metallic sphere of radius $R$ has been charged to a potential of $V=100$ volt. A thin hemispherical conducting shell has dimensions so that it can just fit on the half of the metallic sphere. The shell is originally grounded. Now, using an insulating handle, it is placed on top of the charged sphere so as to perfectly cover its top half. The shell is removed from the sphere and again grounded. After this the shell is again placed on the sphere, removed and then grounded. The process is continued till the potential of the sphere becomes $V^{\prime }=6.25$ volt. How many times the shell was placed on the sphere?

Answer 1

Answer: 4

Charge on a conductor will always be on its outer surface. Shell is thin and fits perfectly over the sphere. Half the charge on sphere will reside on the shell. As the shell is removed, the charge on it also goes away with it. When grounded, the shell will give away all its charge.
Every time shell is mounted and removed, the charge on sphere becomes half (or its potential becomes half)
$\therefore \frac{100}{2^n}=6.25$
$\Rightarrow n=4$