Question

A uniform sphere has radius R. A sphere of diameter R is cut from its edge as shown. Then the diste
centre of mass of remaining portion from
the centre of mass of the original sphere is
(1) R7
(2) R/14
(3) 2R/7
(4) R/18​

Answer 1

(2) R/14

Explanation

Assume

s =  distance between centre of mass from the original centre of the sphere, after cutting the small sphere from it.

d =  density of the sphere.

Mass of large full sphere  = $\frac {4}{3} \times \pi r^3 \times d$

Mass of small sphere cut from its edge = $\frac {4}{3} \times \pi (\frac {r}{2})^3 \times d$

Mass of the remaining portion = $\frac {7}{6} \pi r^3 \times d$

The position of the COM of full sphere = 0

= $-s \times \frac{7}{6}\pi r^3d + \frac{r}{2} \times \frac{4}{3}\pi (\frac{r}{2})^3 \times d = 0$

$s = \frac{r}{14}$

Answer 2

Answer:

r/14.....................