Gravitational potential energy of mass mm
U=-(GMm)/rU=−GMmr
G=G= Universal gravitational constant
M=M=mass of earth
m=m= mass of object
r=r=distance between center of Earth and center of object
Gravitational potential energy on the surface of earth (r=R)(r=R)
U_1=-(GMm)/RU1=−GMmR
Gravitational potential energy on the height R/2R2 rom the surface of earth (r=R+R/2=3R/2)(r=R+R2=3R2)
U_2=-(GMm)/((3R)/2)=-2/3(GMm)/RU2=−GMm3R2=−23GMmR
work done to send a body of mass m from earth surface to height R/2
="change in potential energy of object"=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