A conducting sphere of radius 5 cm is charged to 15µC. Another uncharged . . .

Question : A conducting sphere of radius 5 cm is charged to 15µC. Another uncharged sphere of radius 10 cm is allowed to touch it for enough time. After the two are separated, the surface density of the charge on the two spheres will be in the ratio 

a) 2:1

b) 1:2

c) 1:1

d) 3:1

Doubt by Sonali 

Solution :

r₁ = 5cm

r₂ = 10 cm

q=15µC

When both the sphere are touched to each other then charge flow will take place until the potential of both the spheres will become equal to each other. 

V₁=V₂
kq₁/r₁ = kq₂/r₂
q₁/r₁ = q₂/r₂
q₁/q₂ = r₁/r₂ — (1)

Now, 
σ₁/σ₂ = [q₁/4πr₁²]/[q₂/4πr₂²]
σ1/σ2 = (q₁/q₂) ×(r₂²/r₁²)
σ₁/σ₂ = (r₁/r₂)×r₂²/r₁²
σ₁/σ₂ = r₂/r₁
σ₁/σ₂ = 10/5
σ₁/σ₂ = 2/1

σ₁:σ₂ = 2:1

So, a) would be the correct option.