A body weighs 72 N on the surface of the earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface

Options

A. 16 N
B. 28 N
C. 32 N
D. 72 N

Answer

C

Explanation

( c) Weight of the body on the surface of the earth = mg= 72 N
Acceleration due to gravity at height h is
`g_(h)=(gR_(E)^(2))/((R_(E)+h)^(2))=(gR_(E)^(2))/((R_(E)+(R_(E))/(2))^(2))=(4)/(9)g( :.h=(R_(E))/(2))`
Gravitational force on body at height h is
`F=mg_(h)=mxx(4)/(9) g= (4)/(9)xx mg=(4)/(9)xx72=32 N`