Two bodies of 6 kg and 4 kg masses have their velocity  `5hati-2hatj+10hatj` and `10hati-2hatj+5hatk` respectively. Then, the velocity of their centre of mass is

Options

A. `5hati+2hatj-8hatk`
B. `7hati+2hatj-8hatk`
C. `7hati-2hatj+8hatk`
D. `5hati-2hatj+8hatk`

Answer

(c)

Explanation

` M^(2)=4 kg`, `V_(1) = 5i - 2j + 10k`,
`V_(2) = 10hati - 2hatj + 5k`  (given)
  The expression for velocity of centre of mass is given as, `v=(m_(1)v_(1)+m_(2)v_(2))/(m_(1)+v_(2))`
`=(6(5i-2j+10k)+4(10i-2j+5k))/(6+4)`
`=(30i-12j+60k+40i-8j+20k)/(10)`
`(70i-20j+80k)/(10)`
`7i-2j+8k`.