In given figure charge given to outer sphere is Q. Inner . . .

Question : In given figure charge given to outer sphere is Q. Inner sphere is grounded. What will be charge on outer surface of outer sphere.

(1) -Q/2

(2) Q

(3) Q/2

(4) 3Q/2

Doubt by Saatvik 

Solution : 

We know, whenever a conductor is connected to the ground, its potential becomes zero. 

First of let us calculate what is the charge on the inner sphere. Let this charge would be q.

Potential on the surface of Inner sphere due to charge on its own surface

V₁=kq/a

Potential on the surface of inner sphere due to the charge on the outer sphere

V₂=kQ/2a

Total potential on the surface of inner sphere will be zero so, 

V₁+V₂=0

kq/a+kQ/2a=0

kq/a=-kQ/2a

q=-Q/2

In order to maintain the zero potential on the inner sphere, the inner surface of the outer sphere must induce an equal and opposite charge to that of the charge on the outer surface of inner sphere i.e. Q/2.

So, charge left on the inner surface of the outer sphere will be
=Q-Q/2
=Q/2

Hence, (3) Q/2, would be the correct option.