The centre of mass of a body is a point at which the entire mass of the body is supposed to be concentrated. The position vector `overset rarr(r )` of c.m of the system of tow particles of masses `m_(1)` and `m_(2)` with position vectors `overset rarr(r_(1))` and `overset rarr(r_(2))` is given by
`overset rarr(r ) = (m_(1)overset rarr(r_(1)) + m_(2)overset rarr(r_(2)))/(m_(1) + m_(2))`
For an isolated system, where no external force is acting, `overset rarr(v_(cm)) =` constant
Under no circumstances, the velocity of centre of mass of an isolated system can undergo a change
With the help of the comprehension given above, choose the most appropriate alternative for each of the following questions :
Two bodies of masses `1 kg` and `2kg` are located at `(1, 2)` and `(-1, 3)` respectively. the co-ordinates of the cetre of mass are :

Options

A. `(-1, 3)`
B. `(1, 2)`
C. `(-(1)/(3),(8)/(3))`
D. `((1)/(3),(8)/(3))`

Answer

C

Explanation

Here, `m_(1) = 1 kg, m_(2) = 2kg`
`x_(1) = 1, y_(1) = 2 , x_(2) = - 1, y_(2) = 3`
Co-ordinates of the centre of mass are
`x =(m_(1)x_(1) + m_(2)x_(2))/(m_(1) + m_(2)) = (1(1) + 2(-1))/(1+2) = - (1)/(2)`
`y =(m_(1)y_(1) + m_(2)y_(2))/(m_(1) + m_(2)) = (1(2) + 2(3))/(1+2) = - (1)/(2)`