Four particles of masses `m_(1) = 2m , m_(2) = 4 m , m_(3) = m ` and `m_(4)` are placed at four corners of a square . What should be the value of `m_(4)` , so that the centre of mass of all the four particles are exactly at the centre of the square ?

Options

A. 2m
B. 8m
C. 6m
D. None of these

Answer

D

Explanation

`x_(CM) = 0`

or `(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3)+m_(4)) = 0`
or `(2m)(-a)+(4m)(a) + m(a)+m_(4)(-a) = 0`
or `m_(4) = 3m`
Similarly `y_(CM) = 0`
or `(2m)(-a) + 4m(-a) + m(a) + m_(4)(a) = 0`, or `m_94)=5m`
Since, value of `m_(4)` are differeent to satisfy by both `x_(CM)`=0 and `y_(CM) =0`
Hence, it is not possible