Question

As shown in figure, when a spherical cavity (centred at O) of radius 1 is cut out of a uniform sphere of radius R (centred at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, on the surface of the cavity. R can be detemined by the equation :

(1) (R2 – R + 1) (2 – R) = 1

(2) (R2 + R – 1) (2 – R) = 1

(3) (R2 + R + 1) (2 – R) = 1

(4) (R2 – R – 1) (2 – R) = 1

Answer 1

Answer is (3) (R2 + R + 1) (2 – R) = 1

By concept of COM

m1R1 = m2R2

Remaining mass x (2 - R) = cavity mass x (R - I)

(R3 – 1) (2 – R) = R – 1

(R2 + R + 1) (2 – R) = 1