Two identical balls having like charges and placed at a certain distance apart repel each other with a certain force. They are brought in contact and then moved apart to a distance equal to half their initial separation. The force of repulsion between them increases 4.5 times in comparision with the initial value. The ratio of the initial charges of the balls is

Options

A. 2
B. 3
C. 4
D. 6

Answer

A

Explanation

`F.=(K(q_1+q_2)^2)/r^2`
Now F. = 4.5 F
`=(K(q_1+q_2)^2)/r^2=4.5 (Kq_1q_2)/r^2`
`implies(q_1+q_2)^2=4.5 q_1q_2`
`implies q_1^2 +q_2^2 =2q_1q_2 = 4.5 q_1q_2`
`implies q_1^2 +q_2^2 -2.5 q_1q_2=0`
`= (q_1/q_2)^2+1-2.5 (q_1)/q_2=0`
`q_1/q_2 = (+2.5 pmsqrt(6.25 -4))/2`
`=(2.5 pm 1.5)/2= 2,(1)/2`