A block of mass `5 kg` having charge `q` is attached to a spring of constant `K = 10^(4) N//m`. A charge `-q` is placed below the block at separation `0.5 m`. If the maximum elongation of spring is `0.5 m`. If the maximum elongation of spring is `0.1 m`, find `q`. Assume the initial elongation of spring is zero.

Explanation

Energy conservation between `①` and `②`
`mg(0.5) + (1)/( 4 pi in_(0)) ((q) (-q))/(0.5) = mg (0.4)`
`+ (1)/(4pi in_(0)) + ((q) (-q))/(0.4) + (1)/(2) K (0.1)^(2)`
`mg(0.1) - (1)/(2) K (0.1)^(2)= (q^(2))/(4 pi in_(0)) ((1)/(0.5) - (1)/(0.4))`
`(5 - 50) = -9 xx 10^(9) xx 0.5 q^(2)`
`q^(2) = 10^(-8) rArr q = 10^(-4) C`
`q = 100 mu C`