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 determined by the equation:

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 determined by the equation:

Aicharya · Accepted Answer

M 1 = 4 3 &#960; R 3 &#961; M 2 = 4 3 &#960; 1 3 - &#961; X c o m = M 1 X 1 + M 2 X 2 M 1 + M 2 &#8658; 4 3 &#960; R 3 &#961; 0 + 4 3 &#960; 1 3 - &#961; R - 1 4 3 &#960; R 3 &#961; + 4 3 &#960; 1 3 - &#961; - 2 - R &#8658; R - 1 ( R 3 - 1 ) = 2 - R R &#8800; 1 R - 1 R - 1 R 2 + R + 1 = 2 - 1 R 2 + R + 1 2 - R = 1 Alternative: M r e m a i n i n g 2 - R = M c a v i t y 1 - R &#8658; R 3 - 1 3 2 - R = 1 3 R - 1 &#8658; R 2 + R + 1 2 - R = 1

As shown in figure. When a spherical cavity (centred at O ) of radius 1 is cut out of a uniform sphere of…

Solution