A body of mass m is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be
$3 m g R$
$\frac{1}{3} m g R$
$2 m g R$
$\frac{2}{3} m g R$

Question

A body of mass m is taken from the earth-s surface to the height equal to twice the radius -R- of the earth- The change in potential energy of body will be3 mg Rdfrac -1-3- mg R2 mg Rdfrac -2-3- mg R

Toppr Admin · Accepted Answer

From work-energy theorem- work done - change in potential energy-Work done - -x222B-3RRGmMx2dx-2GmM3R-2mgR3-xA0-Please note that the gravitational force will necessarily vary over this height because it is comparable with earth-apos-s radius-

A body of mass m is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be3mgR13mgR2mgR23mgR

From work-energy theorem, work done = change in potential energy.Work done = ∫3RRGmMx2dx=2GmM3R=2mgR3. Please note that the gravitational force will necessarily vary over this height because it is comparable with earth's radius.

A body of mass m is taken from the earth's surface to the height equal to twice the radius (R) of the earth. The change in potential energy of body will be
$3 m g R$
$\frac{1}{3} m g R$
$2 m g R$
$\frac{2}{3} m g R$

From work-energy theorem, work done = change in potential energy.
Work done = $\int_{R}^{3 R} \frac{G m M}{x^{2}} d x = \frac{2 G m M}{3 R} = \frac{2 m g R}{3}$ .

Please note that the gravitational force will necessarily vary over this height because it is comparable with earth's radius.