# If  g  is the acceleration due to gravity on the earth's surface,  the gain in the potential energy of an object of mass  m   raised from the surface of the earth to   a height equal to the radius  R   of the earth is : Option 1) Option 2) Option 3) Option 4)

As we learnt in

$\dpi{100} Force \; on \; object\; =\frac{GMm}{x^{2}}\; at\: x\; from \; centre \; of \; earth.$

$\dpi{100} \therefore \; \; \; Work\; done=\frac{GMm}{x^{2}}dx$

$\dpi{100} \therefore \; \; \int Work \; done=GMm\int_{R}^{2R}\frac{dx}{x^{2}}$

$\dpi{100} \therefore \; \; \; Potential \; energy\; gained$

$\dpi{100} =GMm\left [ -\frac{1}{x} \right ]_{R}^{2R}=\frac{GMm\times 1}{2R}$

$\dpi{100} \therefore \; \; Gain \; in \; P.E.$

$\dpi{100} =\frac{1}{2}mR\left ( \frac{GM}{R^{2}} \right )=\frac{1}{2}mgR\; \; \;\; \; \; \; \; \; \; \left [ \because g=\frac{GM}{R^{2}} \right ]$

Work done against gravity when 'h' is not negligible -

height above surface of earth

- wherein

if

if

times

Option 1)

Incorrect

Option 2)

Correct

Option 3)

Incorrect

Option 4)

Incorrect

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
##### Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
##### Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
##### Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 24999/-