Question #159c0

1 Answer
Sep 23, 2017

W=1/3(GMm)/R=(mgR)/3

Explanation:

Gravitational potential energy of mass m
U=-(GMm)/r
G= Universal gravitational constant
M=mass of earth
m= mass of object
r=distance between center of Earth and center of object

Gravitational potential energy on the surface of earth (r=R)
U_1=-(GMm)/R

Gravitational potential energy on the height R/2 rom the surface of earth (r=R+R/2=3R/2)
U_2=-(GMm)/((3R)/2)=-2/3(GMm)/R
work done to send a body of mass m from earth surface to height R/2
="change in potential energy of object"
W=DeltaU=U_2-U_1
W=-2/3(GMm)/R-(-(GMm)/R)=-2/3(GMm)/R+(GMm)/R
W=(GMm)/R (1-2/3)
W=1/3(GMm)/R

We know that relation between Universal gravitational constant and acceleration due to gravityg is GM=gR^2

W=1/3(gR^2m)/R=(mgR)/3