Two bodies of mass 1 kg and 3 kg have position vectors `hati+2hatj+hatk and -3hati-2hatj+hatk` respectively. The centre of mass of this system has a position vector.

Options

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

Answer

A

Explanation

Mass `m_(1)andm_(2)` and position vector `vec(r_(1)) and vec(r_(2))` of a system have centre of mass.
`vec(r_(CM))=(m_(1)vec(r_(1))+m_(2)vec(r_(2)))/(m_(1)+m_(2))`
In this formula, `m_(1)=1,m_(2)=3,vec(r_(1))=hati+2hatj+hatk and vec(r_(2))=-3hati-2hatj+hatk`
`vec(r_(CM))=(1(hati+2hatj+hatk)+3(-3hati-2hatj+hatk))/(1+3)`
`=(1)/(4)[-8hati-4hatj+4hatk]`
`=-2hati-hatj+hatk`