Centre of mass of 3 particles 10 kg, 20 kg and 30 kg is at (0, 0, 0). Where should a particle of mass 40 kg be placed so that the combination centre of mass will be at (3,3,3)

Options

A. (0,0,0)
B. (7.5, 7.5, 7.5)
C. (1,2,3)
D. (4,4,4)

Answer

B

Explanation

Total mass of particles `(m_(1))= 10 + 20 + 30 = 60kg`
`x_(1) = 0, y_(1)= 0, z_(1)= 0 and m_(2)= 40g, (x_(2), y_(2), z_(2))`
`X_(CM)= 3, Y_(CM)= 3, Z_(CM)= 3`
`X_(CM)= (m_(1) x_(1) + m_(2) x_(2))/(m_(1) + m_(2)) rArr 3= (60 xx 0 + 40 xx x_(2))/(100)`
`rArr x_(2)= (300)/(40)= 7.5`
Similarly, `y_(2)= 7.5 and z_(2)= 7.5`