Four particles `A,B,C` and `D` with masses `m_(A)=m,m_(B)=2m, m_(C)=3m` and `m_(D)=4m` are at the comers of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is :

Options

A. `a/5 (hati - hatj)`
B. `a(hati + hatj)`
C. `a/5 (hati + hatj)`
D. zero

Answer

A

Explanation

`bar(a)_(CM) = (m_1bara_1+ m_3bara_2 + m_3bara_3 + m_4bara_4)/(m_1 + m_2 + m_3 + m_4) = (m (-a hati) + 2m(a hatj) + 3m(a hati) + 4m(-a hatj))/(m + 2m + 3m + 4m) = (2a hati - 2ahatj)/(10) = a/5 (hati - hatj)`