A body of mass m taken from the earth's surface to the height h = 3R (R = Radius of earth) The change in gravitational potential energy of the body will be ........

A body of mass m taken from the earth's surface to the height h = 3R (

1.	A body of mass m taken from the earth's surface to the height h = 3R (R = Radius of earth) The change in gravitational potential energy of the body will be ........
Answer» `2/3 MGR` `3/4 mgR` `(mgR)/2` `(mgR)/4` Solution :`implies` One the surface of EARTH `U_1 = -(GMm)/R` (R = Radius of earth M = MASS of earth) For height h = 3R FORM the surface of earth and distance r form the centre of earth `r = R + h = R + 3R = UR` `U_2 =-(GMm)/(4R)` `U_2-U_1 =-(GMm)/(4R)+(GMm)/R` `=(GMm)/R [-1/4 +1]` `=(GMm)/R [-(1+4)/4]` `= (3GMm)/(4R)` Putting `GM=gR^2` `U_2 -U_1 = (3gR^2m)/(4R) = 3/4 mgR`