Question

A uniform circular disc has radius r. A square portion of diagonal r is cut from it. The centre of mass of the remaining portion (from the centre) is at

Answer 1

Hey friend,

Consider a circular sheet with radius r and mass M. A sqaure sheet with diagonal r and mass m is cut off from it.

Assuming centre of mass of circle to be origin i.e. at 0.

Centre of mass of square sheet will be at distance of r/2 from it.

Side of square = r/√2

Area of square = r^2 /2

Assuming metal sheet as uniform density

Mass of square m = M ×(r^2 /2)/(πr^2) =M/2π

Centre of mass of remaining sheet =

x = [M×0-(M/2π × r/2)]/ [M-M/2π]

x = -r/2(2π-1)

Hence, centre of mass of remaining part lies at a distance r/2(2π-1) towards right from centre of the circle.

Hope this helps...

Answer 2

Answer:

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