A spherical hole of radius R/2 is excavated from the asteroid of mass M as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is
Answer & explanation
Correct answer: option 2
gnet = g1 - g2
g1 = gravitational attraction due to sphere of radius R
g2 = gravitational attraction due to hollow sphere of radius R/2 at surface.
$=\frac{G M}{R^2}-\frac{G\left[\frac{M}{(4 / 3) \pi R^3}\right] \frac{4}{3} \pi\left(\frac{R}{2}\right)^3}{(R / 2)^2}=\frac{G M}{2 R^2}$