Question

For years together, people thought that hell is located inside earth. Assume that hell is a spherical bubble created inside earth. It is completely evacuated to make sinful people feel suffocated. It has a radius $R/4$ and is located as shown. ( $C$ is earth's centre). What is the distance of centre of mass of the resulting body from $C$ (in $km$ ). Assume that earth's radius is $6300km$.

Answer 1

Answer: 25

$M_0=r\times \frac{4}{3}\pi R^3$
$M_c=\rho \times \frac{4}{3}\pi {\left(\frac{R}{4}\right)}^3=\frac{M_0}{64}$
$x_c=\frac{M_0\times 0-M_c\times \frac{R}{4}}{M_0-M_c}$
$=\frac{\frac{-M_0}{256}R}{M_0-\frac{M_0}{64}}=25km$