Two metallic spheres of radii `1 cm` and `2 cm` are given charges `10^(-2) C` and `5 xx 10^(-2) C` respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is

Options

A. `2xx10^(-2) C`
B. `3xx10^(-2) C`
C. `4xx10^(-2) C`
D. `1xx10^(-2) C`

Answer

B

Explanation

Here, `r_(1) = 1 cm, r_(2) = 3 cm`,
`q_(1) = -10^(-2) C, q_(2) = 5xx10^(-2) C`
When the two spheres are connected by a conducting wire, charge flows second sphere to first sphere till their potentials become equal.If bigger sphere loses charge `x xx 10^(-2)`coulomb, then as `V_(1) = V_(2)`
`:. (k (x -1) 10^(-2))/(1 xx 10^(-2)) = (k (5-x) 10^(-2))/(3xx10^(-2))`
`3x - 3 = 5-x, 4x =8, x = 2`
`:.` Charge left on bigger sphere `= (5-2) 10^(-2) C`
`= 3xx10^(-2) C`