Question

Two particles are moving along the x axis. Particle 1 has a mass m₁ and a velocity v₁ = +4.5 m/s. Particle 2 has a mass m₂ and a velocity v₂ = -7.3 m/s. The velocity of the center of mass of these two particles is zero. In other words, the center of mass of the particles remains stationary, even though each particle is moving. Find the ratio m₁/m₂ of the masses of the particles.

Answer 1

m1v1=m2v2

m1/m2=v2/v1

= 7.3/4.5

=1.622

Answer 2

since centre of mass is stationary

the particles are moving in opposite direction with equal momentum

m1v1 = m2v2

m1*4.5 = m2*7.3

m1/m2 = 1.622

Answer 3

Xcm = [m1X1 +m2X2]/(m1+m2)

dXcm/dt = [ 1/(m1+m2)   ] * (m1v1+m2v2)

0 = [ 1/(m1+m2)    ] *(4.5m1 -7.3m2)

m1/m2 = 7.3/4.5 = 1.622

Answer 4

SINCE C.M IS AT REST , SO NO FORCE IS ACTING ON C.M

SO MOMENTUM IS CONSERVED

SO,

M1V1+M2V2=0

M1X4.5-M2X7.3=0

M1/M2=7.3/4.5=1.62

Answer 5

velocity of the center of mass =m1v1+m2v2=0

or, m1v1+m2v2=0

m1*4.5-m2*7.3=0

4.5m1=7.3m2

m1/m2=7.3/4.5=1.622