The centre of mass of a system of three particles of masses 1 g, 2 g and 3 g is taken as the origin of a coordinate system. The position vector of a fourth particle of mass 4 g such that the centre of mass of the four particle system lies at the point `(1, 2, 3)` is `alpha(hati+2hatj+3hatk)`, where `alpha` is a constant. The value of `alpha` is

Options

A. `10//3`
B. `5//2`
C. `1//2`
D. `2//5`

Answer

B

Explanation

Mass of three particle `(m_(1))=1+2+3=6g`
`{:(x_(CM_(1))=0,y_(CM_(1))=0,z_(CM_(1))=0):}`
and `{:(m_(2)=4g, x_(CM_(2))=alpha, y_(CM_(2)=2alpha,,z_(CM_(2))=3alpha)):}`
Now
`X_(CM)=1, Y_(CM)=2, Z_(CM)=3`
Now,
`X_(CM)=(6xx0+4xxalpha)/(6+4)=(4alpha)/(10)=(2)/(5)alpha`
implies `1=(2alpha)/(5)impliesalpha=(5)/(2)` .