A circular disc of radius R is removed from one end of a bigger circular disc of radius 2 R . The centre of mass of the new disc is at a distance R from the centre of the bigger disc. The value of is

Step-by-step solution

Let, mass of entire disc =M Mass per unit area = M (2 R)^2 = M 4 R^2 Mass of removed disc of radius R , M₁= M 4 R^2 R^2= M 4 Mass of remaining disc, M₂=M- M 4 = 3 M 4 Center of mass of removed disc is C₁ and centre of mass of remaining new disc is C₂ . And centre of mass of combination of M₁ and M₂ will be at C(0,0) . aligned & M₁ x₁-M₂ x₂ M₁-M₂ =0 & M₁ x₁=M₂ x₂ & M 4 R= 3 M 4 ( R) = 1 3 aligned