Two objects of masses 10 kg and 2 kg are moving with . . .

Question : Two objects of masses 10 kg and 2 kg are moving with velocities (2i-7j+3k) m/s and (-10i+35j-3k) m/s respectively. Calculate the velocity and acceleration of their centre of mass.

Doubt by Zoha
DAV 2023

Solution : 

m₁=10 kg

m₂ = 2kg

v₁=(2i-7j+3k) m/s

v₂=(-10i+35j-3k) m/s 

V_cm = (m₁v₁+m₂v₂)/(m₁+m₂)

        = [10(2i-7j+3k)+2(-10i+35j-3k)]/(10+2)
        = [20i-70j+30k-20i+70j-6k]/12

        = 24k/12
        = 2k m/s

Velocity of centre of mass is a constant hence the acceleration of the centre of mass will be zero.