From a circular disc of radius 2 R , a smaller circular disc is cut with radius of the larger disc as its diameter. The centre of the hole is at a distance of R from the centre of the original disc. The distance of the centre of mass of the remaining portion from the centre is:

Step-by-step solution

Let the radius of the original disc be r₁ = 2R . The area of the original disc is A₁ = (2R)^2 = 4 R^2 . The smaller disc cut from it has a diameter equal to the radius of the larger disc, so its diameter is 2R and its radius is r₂ = R . The area of the smaller disc is A₂ = R^2 . Let the centre of the original disc be at the origin (0, 0) . The centre of the smaller disc is at a distance R from the origin, so its coordinates are (R, 0) . The centre of mass of the remaining portion is given by the formula X_ cm = A₁