Question

From a sphere of radius $1m$, a sphere of radius $0.5m$ is removed from the edge. The position of centre of mass of the remaining
portion from centre of the sphere is

• A. $\frac{13}{6}m$
• B. $\frac{16}{13}m$
• C. $\frac{14}{13}m$
• D. $\frac{1}{14}m$

Answer 1

The correct option is D $\frac{1}{14}m$

Let us consider m1 as sphere of 0.5 radius and m2 as the remaining portion of sphere after removing m1

Let origin be at centre of sphere of radius 1m

x1 and x2 be the x components of centre of masses m1 and m2 respectively

x1 =0.5

x2=x

Let density of sphere be d

m1 = d$\frac{4}{3}\times \pi \times {0.5}^3$

m2=d$\frac{4}{3}\times \pi \times (1^3-{0.5}^3)$

centre of mass of m1 and m2 is at origin

0=d$\frac{4}{3}\times \pi \times \left({0.5}^3\right)\times 0.5$+d$\frac{4}{3}\times \pi \times (1^3-{0.5}^3)\times x$

x=-$\frac{1}{14}$m