Answer

Verified

383.7k+ views

**Hint:**use the gravitational potential energy formula, which is given by

$ U=-\dfrac{GMm}{r} $ Here, m is mass of object ,

M is mass of earth

At the surface of earth r = R

Then gravitational potential energy, $ $ $ U=-\dfrac{GMm}{R} $

Change in potential energy,

$ \Delta u={{u}_{f}}-{{u}_{i}} $

Use the above formula to find the required result.

**Complete step by step solution**

We have given the body of mass m,

And mass of earth by M

At the surface of earth, Gravitational potential energy is given by,

$ {{U}_{i}}=-\dfrac{GMm}{R} $

If h is the height from the surface then, r = h+R , here, r is distance taken from the surface of earth.

Also, we have given height is equal to twice the radius of earth i.e., h = 2R

Then, r = $ \text{2R}+\text{R} $

= 3R

The final gravitational potential energy is given by,

$ {{U}_{f}}=-\dfrac{GMm}{3R} $

Change in potential energy is given by,

$ \Delta u={{u}_{f}}-{{u}_{i}} $

$ =-\dfrac{GMm}{3R}-\text{(}\dfrac{-GMm}{R}) $

$ =-\dfrac{GMm}{3R}+\dfrac{GMm}{R} $

$ \Delta u=\dfrac{2}{3}\dfrac{GMm}{R} $ -------- (1)

Use the relation between g(gravity) and G (Gravitational constant).

$ g=\dfrac{GM}{{{R}^{2}}} $

Hence, The eq. (1) becomes

$ \Delta u=\dfrac{2}{3}\times \dfrac{g{{R}^{2}}m}{R} $

$ \Delta u=\dfrac{2}{3}mgR $ this is the required result.

**So option (D) is the correct answer.**

**Note**

Negative sign show that the potential energy is due to attractive gravitational force exerted by earth on the body

We know $ u=-\dfrac{GMm}{r} $ , if the value of r increases, the gravitational potential energy increases as it becomes less negative. When r is infinity, gravitational potential energy becomes zero.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE