Assertion: An isolated system consist of two particles of equal masses `m = 10 gm` and charged `q_(1) =+1muC` and `q_(2) =-1muC` as shown in figure. The initial separation of both charges is `l = 1m`. Both the charges are given initial velocities `v_(1) = 1m//s` and `v_(2) = 2m//s` towards right. then the maximum separation between the charges is infinity.

Reason: The total energy (Kinetic energy + electrostatic potential energy) of given two particle system is positive and initial velocity of separation is positive.

Options

A. If both assertion and reason are true and reson is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion and reason both are false.

Answer

A

Explanation

`K.E.` of system of two particles
`(1)/(2)mv_(1)^(2) + (1)/(2)mv_(2)^(2) = (1)/(2) 10 xx 10^(-3) xx 1^(2) + (1)/(2) 10 xx 10^(-3) xx 2^(2) = 2.5 xx 10^(-2) J`
Electrostatic potential energy of system of two particles is
`= (1)/(4pi epsilon_(0)) (q_(1)q_(2))/(l) = 9 xx 10^(9) xx (1 xx 10^(-6) xx (-1) xx 10^(-6))/(1)`
`=-9 xx 10^(-3) J`
`:.` Total energy of system `= 2.5 xx 10^(-2) - 9 xx 10^(-3)` positive
Since the total energy of system is positive, the system is unbounded. therefore maximum distance between particles is infinity.