Two strange particles A and B in space, exert no force on each other when they are at a separation greater than `x_(0) = 1.0` m. When they are at a distance less than `x_(0)`, they repel one another along the line joining them. The repulsion force is constant and does not depend on the distance between the particles. This repulsive force produces an acceleration of `6 ms^(–2)` in A and `2 ms^(–2)` in B when the particles are at separation less than `x_(0)`. In one experiment particle B is projected towards A with a velocity of `2 ms^(–1)` from a large distance so as to hit A head on. The particle A is originally at rest and the system of two particles do not experience any external force.
(a) Find the ratio of mass of A to that of B.
(b) Find the minimum distance between the particles during subsequent motion. (c) Find the final velocity of the two particles.

Answer

(a) `(m_(A))/(m_(B)) = (1)/(3)`
`X_("min") = 0. 75 m `
(c) `V'_(A) = ((3)/(2) + (3)/(sqrt2))ms^(-1) ; V'_(B) = ((3)/(2) - (1)/(sqrt2))ms^(-1)`