A body .A. with a momentum .P. collides with another identical stationery body .B. one dimensionally. During the collision, .B. gives an impulse .J. to the body .A.. Then the coefficient of restitution is

A body .A. with a momentum .P. collides with another identical station

1.	A body .A. with a momentum .P. collides with another identical stationery body .B. one dimensionally. During the collision, .B. gives an impulse .J. to the body .A.. Then the coefficient of restitution is
Answer» Solution :According to law of conservation of linear momentum, `m _(1) U _(1) + m_(2) u_(2) = m _(1) V _(1) + m _(2) v _(2)` i.e., `m u + m (0) = mv _(1) + mv _(2) IMPLIES P - P _(1) = P _(2) ` where `P _(2) = J,` GIVEN `therefore` Coefficient of resistution, ` e = (v _(2) -v _(1))/( u ) = (mv _(2) - mv _(1))/( m u ) = (P_(2) - P_(1))/( P )` `= (P _(2) - (P-P_(2)))/( P ) = (2P _(2) - P _(1))/( P ) therefore e = (2 J - P )/(P) = (2J)/(P) -1 `