Question

An object is taken to height 2r above the surface of earth the increase in potential energy is

Answer 1

when the object is placed at surface of earth, potential energy , $U_i=-\frac{GmM}{r}$
where m is mass of the object , M is mass of the earth and r is the radius of the earth.

when the object is placed at height 2r above the surface of earth. potential energy is given by , $U_f=-\frac{GmM}{(r+2r)} = -\frac{GmM}{3r}$

now, change in potential energy, ∆U = $U_f-U_i$

=$-\frac{GmM}{3r}+\frac{GmM}{r}$

=$\frac{2}{3}\frac{GMm}{r}$

= $\frac{2}{3}mgr$ [ as g = GM/r² ]

Answer 2

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Rahul Hotwani asked in Physics

a body of mass m is raised from the earths surface to an altitude equal to the radius(R) of the earth. if g is the gravitational acceleration on earths surface the change in the potential energy of the body is,_______

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Kranav.sharma... answered this
7060 helpful votes in Physics, Class XII-Science

gravitational potential energy of a body of mass 'm' on the surface of the earth  radius 'R' and mass 'M' will be

U = -GMm/R

and at a height equal to earth's radius

U' = -GMm/(R+R) = -GMm/(2R)

so, change in potential energy will be

dU = U - U'

or

dU = -GMm/R - [-GMm/(2R)]

= (-GMm/R)[1 - 1/2]

thus, we get

dU = -GMm/2R