A circular hole is cut from a disc of radius 6 cm in such a way that the radius of the hole is 1 cm and the centre of the hole is at a distance of 3 cm from the centre of the disc. The distance of the centre of mass of the remaining part from the centre of the original disc is

Question

A circular hole is cut from a disc of radius 6 cm in such a way that the radius of the hole is 1 cm and the centre of the hole is at a distance of 3 cm from the centre of the disc. The distance of the centre of mass of the remaining part from the centre of the original disc is, 3 / 35 cm, 1 / 35 cm, 3 / 10 cm, 7 / 35 cm

MARKS App · Accepted Answer

For the calculation of the position of centre of mass, cut off mass is taken as negative. The mass of disc is m 1 = π r 1 2 σ = π 6 2 σ = 36 π σ where σ = surface mass density. The mass of cut out portion is m 2 = π 1 2 σ = π σ x cm = m 1 x 1 - m 2 x 2 m 1 - m 2 Taking origin at the centre of disc, x 1 = 0, x 2 = 3 cm x cm = 36 π σ × 0 - π σ × 3 3 6 π σ - π σ = - 3 π σ 3 5 π σ = - 3 3 5 cm

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