Four particle of masses m1=2 m , m2 =4 m , m3=m and m4 are placed at four corners of a square. What should be the value of m4 so that the centres of mass of all the four particles are exactly at the centre of the square?

Question

Four particle of masses m1=2 m , m2 =4 m , m3=m and m4 are placed at four corners of a square. What should be the value of m4 so that the centres of mass of all the four particles are exactly at the centre of the square? (A) 3 m (B) 5 m (C) 8 m (D) none of these

Tardigrade Admin · Accepted Answer

Let side of square is a. xc m=(a/2)=(m1 × 0+m2 × a+m3 × a+m4 × 0/m1+m2+m3+m4) solve to get m4=3 m yc m=(a/2)=(m1 × 0+m2 × 0+m3 × a+m4 × a/m1+m2+m3+m4) solve to get m4=5 m They are contradicting, so it is not possible to have centre of mass at the centre of square.

Q. Four particle of masses m1​=2m,m2​ =4m,m3​=m and m4​ are placed at four corners of a square. What should be the value of m4​ so that the centres of mass of all the four particles are exactly at the centre of the square?

3 m

5 m

8 m

none of these

Q. 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 particles are exactly at the centre of the square?