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The centre of mass of a system of three ...

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

A

`10//3`

B

`5//2`

C

`1//2`

D

`2//5`

Text Solution

Verified by Experts

The correct Answer is:
B
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)= a, y_(CM)_(2)= 2a, z_(CM)_(2)= 3a`
Now, `X_(CM)= 1, Y_(CM)= 2, Z_(CM)= 3`
Now, `X_(CM)= (6 xx 0 + 4 xx a)/(6+ 4)= (4a)/(10)= (2)/(5) a`
`rArr 1= ((2a)/(5)) rArr a = (5)/(2)`
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