Three bodies of masses 3kg, 2kg and 1 kg kept at points `(3hati+2hatj),(5hatj+hatk)` and `(2hati+hatk)` respectively. Then the position vector of their centre of mass is given by

Options

A. `vecR_(cm)=(11hati)/6+3/8hatj+2hatk`
B. `vecR_(cm)=(11hati)/6+8/3hatj+(hatk)/2`
C. `vecR_(cm)=(7hati)/6+5/8hatj+2hatk`
D. `vecR_(CM)=(11hati)/6+8/5hatj+3hatk`

Answer

B

Explanation

`vec(R) cm = (m_(1)vec(r_(1))+m_(2)vec(r_(2))+m_(3)vec(r_(3)))`
`=(3(3hati+2hatj)+2(5hatj+hatk)+1(2hati+hatk))/(3+2+1)`
`=(9hati+6hatj+10hatj+2hatk+2hati+hatk)/(6)`
`=(11hati+16hatj+3hatk)/(6)`
`:. vecRcm=(11hati)/(6) +8/3 hatj+1/2hatk`