Four particle of masses `m_1 = 2 m, 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 centres of mass of all the four particle are exactly at the centre of the square ?

Options

A. 3 m
B. 5 m
C. 8 m
D. none of these

Answer

D

Explanation

(d) Let side of square is `a`.
`x_(cm) = (a)/(2) = (m_1 xx 0 + m_2 xxa + m_3 xx a + m_4 xx a)/(m_1 + m_2 + m_3 + m_4)`
solve to get `m_4 = 3 m`
`y_(cm) = (a)/(2) = (m_1 xx0 +m_2 xx 0 + m_3 xx a + m_4 xx a)/(m_1 + m_2 + m_3 + m_4)`
solve to get `m_4 = 5 m`
They are contradicting, so it is not possible to have centre of mass at the centre of square.