Particles of masses 10 g and 20 g have position vectors `(5,3,0) and (2,0,3)` respectively. The position vector of their centre of mass is ………… cm.

Options

A. `(1,2,3)`
B. `(3,1,2)`
C. `(2,3,1)`
D. `(3,2,1)`

Answer

B

Explanation

`m_(1)=10g,vec(r_(1))=[5,30]cm`
`m_(2)=20g,vec(r_(2))=[2,0,3]cm`
`therefore vec(r)_(cm)=(m_(1)vec(r_(1))+m_(2)vec(r_(2)))/(m_(1)+m_(2))=(10(5,3,0)+20(2,0,3))/(10+20)`
`therefore vec(r)_(cm)=((50,30,0)+(40,0,60))/(30)=(("90, 30, 60"))/(30)`
`therefore vec(r)_(cm)=(3,1,2)cm`