Question

a body of mass m kg collides elastically with another body at rest and Then continues to move in the original direction with one half of its original Speed.what is the mass of the Target body?

Answer 1

Let mass of target body is M.

as external force acting on the system of masses is zero.

from law of conservation of linear momentum,

initial momentum = final momentum

initial momentum = mv

where v is velocity of body of mass m.

final momentum = momentum of mass m + momentum of mass x

= mv/2 + M × v2

[ here v2 is velocity of mass M after collision ]

now, mv = mv/2 + Mv2

or, mv/2 = Mv2 ......(1)

from conservation of energy theorem,

initial kinetic energy = final kinetic energy

or, 1/2 mv² = 1/2 m(v/2)² + 1/2Mv2²

or, 1/2 mv² = 1/8 mv² + 1/2(Mv2)²/M

or, 3/8 mv² = 1/2 (mv/2)²/M

or, 3/8 mv² = 1/8 m²v²/M

or, 3M = m

or, M = m/3

hence, mass of target body is m/3.