Question

Four particles of masses m1=1, m2=2, m3=1 and m4 are placed at the four corners of the square. The mass m4 is required, so that the centre of mass of all the four particle is exactly at the centre of the square is

Answer 1

Answer:

mass of m₄ required is 2 units.

Explanation:

Let one vertex of square of side 'a' units  be located at origin.

The co- ordinates of four masses are m₁ (0, 0) , m₂ (a , 0), m₃ (a, a) and

m₄ (0, a )

Co ordinates of centre of mass are (a/2, a/2 )

x co-ordinate of centre of mass $r_{CM}$  = ∑ m₁x₁/M

 a/2= [1 x 0 + 2 x a + 1 x a + m₄ x 0]/(4 + m₄)  

a/2 = 3a/(4 + m₄)

4 + m₄ = 6

      m₄ = 2 units