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The coordinates of the positions of part...

The coordinates of the positions of particles of mass 7, 4 and 10 gm are (1, 5,-3) , (2, 5, 7) and (3, 3,-1) respectively. Find the position of the center of mass of the system?

A

`(-(15)/(7),(85)/(17),(1)/(7))cm`

B

`((15)/(7),-(85)/(17),(1)/(7))cm`

C

`((15)/(7),(85)/(21),-(1)/(7))cm`

D

`((15)/(7),(85)/(21),(7)/(3))cm`

Text Solution

Verified by Experts

The correct Answer is:
C
`m_(1)=7 gm, m_(2)=4 gm, m_(3)=10 gm` and `vec(r )_(1)=(hat(i)+5hat(j)-3hat(k)), r_(2)=(2i+5j+7k), r_(3)=(3hat(i)+3hat(j)-hat(k))`
Position vector of center mass `vec(r )=(7(hat(i)+5hat(j)-3hat(k))+4(2hat(i)+5hat(j)+7hat(k))+10(3hat(i)+3hat(j)-hat(k)))/(7+4+10)=((45hat(i)+85hat(j)-3hat(k)))/(21)`
`rArr vec(r )=(15)/(7)hat(i)+(85)/(21)hat(j)-(1)/(7)hat(k)`. So coordinates of centre of mass `[(15)/(7),(85)/(21),(-1)/(7)]`.
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