A spherical Uparrow mathrm-o-mathrm-l-mathrm-e- of radius mathrm-R-2 is excavated from mathrm-t-Uparrow mathrm-e- asteroid of massmathrm-M- as shown in fig- mathrm-T-Uparrow mathrm-e- gravitational acceleration a point on mathrm-t-Uparrow mathrm-e-surf ace of mathrm-t-Uparrow mathrm-e- asteroid just above mathrm-t-Uparrow mathrm-e- excavation is -mathrm-G-mathrm-M-mathrm-R-2-mathrm-G-mathrm-M-2mathrm-R-2-mathrm-G-mathrm-M-8mathrm-R-2-7mathrm-g-mathrm-W-8mathrm-R-2-

Question

Toppr Admin · Accepted Answer

The energy at centre of hole is energy due to empty part $(ε_{1})$ plus energy due to remaining mass $(ε_{2})$ .
The energy due to empty mass $= 0$ at center of the empty portion
$E = E_{1} + E_{2}$
$E_{2} = E - E_{1}$
$= \frac{1}{8} \frac{G M}{{(\frac{R}{2})}^{2}}$
$E = \frac{G M}{{2 R}^{2}}$

A spherical ⇑ole of radius R/2 is excavated from t⇑e asteroid of massM as shown in fig. T⇑e gravitational acceleration at a point on t⇑esurf ace of t⇑e asteroid just above t⇑e excavation is :GM/R2GM/2R2GM/8R27gW8R2

The energy at centre of hole is energy due to empty part (ε1) plus energy due to remaining mass (ε2).The energy due to empty mass =0 at center of the empty portionE=E1+E2E2=E−E1 =18GM(R2)2E=GM2R2

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

$G M / R^{2}$
$G M / 2 R^{2}$
$G M / 8 R^{2}$
$7 g W 8 R^{2}$

The energy at centre of hole is energy due to empty part $(ε_{1})$ plus energy due to remaining mass $(ε_{2})$ .
The energy due to empty mass $= 0$ at center of the empty portion
$E = E_{1} + E_{2}$
$E_{2} = E - E_{1}$
$= \frac{1}{8} \frac{G M}{{(\frac{R}{2})}^{2}}$
$E = \frac{G M}{{2 R}^{2}}$