Question

a uniform circular disc 24 cm in diameter has a circular hole 6 CM in diameter cut into it the centre of the whole is at a distance of 6 cm from the centre of the disc find the position of centre of gravitation​

Answer 1

Answer:

Radius of circular disc, R = D/2 = 24 / 2 = 12 cm [diameter is given as 24 cm]

The radius of the circular hole, r = d/2 = 6 /2 = 3 cm [diameter is given as 6 cm]

The distance from the centre of the hole and the centre of the disc = 6 cm

Let the mass of the disc be “M”

Then,  

Mass of portion cut out from the disc,

m = [M / R²] * r² = [M / 12²] * 3² = M / 16

After the circular hole of mass “m” is cut out from the circular disc, the remaining portion can be considered as a system of two masses “M” and “- m” = - M/16.

Now,  

The position of the centre of gravity of the resulting disc is given as,

= [(M * 0) – (M/16) * 6] / [M + (-M/16)]

= – (6M/16) * (16 /15M)

= - 0.4 cm

[here, the negative sign denotes that the centre of gravity lies in the opposite direction of the original centre of mass of the disc at a distance of 0.4 cm ]