Two particles of mass 1 kg and 3 kg have position vectors `2hati + 3hatj+4hatk` and `-2hati+ 3hatj - 4hatk` respectively. The centre of mass, has a position vector

Options

A. `hati+3hatj-2hatk`
B. `-hati-3hatj-2hatk`
C. `-hati+3hatj+2hatk`
D. `-hati+3hatj-2hatk`

Answer

(d)

Explanation

Centre of mass,
`r_(cm)=(m_(1)r_(1)+m_(2)r_(2))/(m_(1)+(m_(2)))`
`r_(cm)=([1xx(2hati+3hatj+4hatk)+3(2-2hati+3hati-4hatk)])/(1+3)`
`r_(cm)=(2hati+3hatj+4hatk-6hati+9hatj-12hatk)/(4)`
`r_(cm)=(-4hati+12hatj-8hatk)/(4)`
`because r_(cm)=-hati+3hatj-2hatk`.