A spherical planet (density = `rho`) of radius R has a spherical cavity of radius R/3, as shown
(a) A small body is released at point P. How much time would it take to reach the lower surface of the cavity ?
(b) A small body of mass m is placed at a distance 2R above point P, on the dotted line extended upwards. What force does the planet exert on the body ?

Answer

(a) `sqrt((3)/(2rho))piG`, (b) `(184)/(1323)MG rho pi R`

Explanation

(a) Net E constant inside covity
`E=(8)/(9)pi rho GR`
So `(2R)/(3)=(1)/(2)at^(2)`
`T = sqrt((2xx2xxR//3)/((4)/(3)piGP(2R)/(3)))=sqrt((3)/(2pi rho G))`
(b) `m[(G.(4)/(3)piR^(3)P)/((3R)^(2))-(G.(4)/(3)pi((R )/(3))^(3)P)/(((7R)/(3))^(2))]=(184)/(1323)MGP pi R`