Question

A spherical $\Uparrow ole$ of radius $R/2$ is excavated from $t\Uparrow e$ asteroid of mass
$M$ as shown in fig. $T\Uparrow e$ gravitational acceleration at a point on $t\Uparrow e$
surf ace of $t\Uparrow e$ asteroid just above $t\Uparrow e$ excavation is :

• A. $GM/R^2$
• B. $GM/2R^2$
• C. $GM/8R^2$
• D. $7gW8R^2$

Answer 1

The correct option is B $GM/2R^2$

The energy at centre of hole is energy due to empty part $\left({\epsilon }_1\right)$ plus energy due to remaining mass $\left({\epsilon }_2\right)$.

The energy due to empty mass $=0$ at center of the empty portion

$E=E_1+E_2$

$E_2=E-E_1$

$=\frac{1}{8}\frac{GM}{{\left(\frac{R}{2}\right)}^2}$

$E=\frac{GM}{{2R}^2}$