The gravitational potential energy of a particle of mass $$m$$ increases by $$mgh,$$ when it is raised through a height $$h$$ in a uniform gravitational field "$$g$$". If a particle of mass $$m$$ is raised through a height $$h$$ in the earth's gravitational field ($$g$$: the field on the earth's surface) and the increase in gravitational potential energy is $$U$$, then:

 1 $$U > mgh$$ 2 $$U < mgh$$ 3 $$U = mgh$$ 4 any of the above may be true depending on the value of $$h,$$ considered relative to the radius of the earth.
Subtopic:  Gravitational Potential Energy |
From NCERT
Hints

Two uniform solid spheres of equal radii $${R},$$ but mass $${M}$$ and $$4M$$ have a centre to centre separation $$6R,$$ as shown in the figure. The two spheres are held fixed. A projectile of mass $$m$$ is projected from the surface of the sphere of mass $$M$$ directly towards the centre of the second sphere. The expression for the minimum speed $$v$$ of the projectile so that it reaches the surface of the second sphere is:

1. $$\left(\frac{3 {GM}}{5 {R}}\right)^{1 / 2}$$
2. $$\left(\frac{2 {GM}}{5 {R}}\right)^{1 / 2}$$
3. $$\left(\frac{3 {GM}}{2 {R}}\right)^{1 / 2}$$
4. $$\left(\frac{5 {GM}}{3 {R}}\right)^{1 / 2}$$

Subtopic:  Gravitational Potential Energy |
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A rocket is fired vertically with a speed of $$5$$ km/s from the earth’s surface. How far from the earth does the rocket go before returning to the earth?
1. $$8\times10^6$$ m
2. $$1.6\times10^6$$ m
3. $$6.4\times10^6$$ m
4. $$12\times10^6$$ m

Subtopic:  Gravitational Potential Energy |
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints

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 the body will be:

 1 $$\frac{2}{3}mgR$$ 2 $$3mgR$$ 3 $$\frac{1}{3}mgR$$ 4 $$2mgR$$
Subtopic:  Gravitational Potential Energy |
76%
From NCERT
AIPMT - 2013
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A satellite of mass $$m$$ is orbiting the earth (of radius $$R$$) at a height $$h$$ from its surface. What is the total energy of the satellite in terms of $$g_0?$$
($$g_0$$ is the value of acceleration due to gravity at the earth's surface)

 1 $$\frac{mg_0R^2}{2(R+h)}$$ 2 $$-\frac{mg_0R^2}{2(R+h)}$$ 3 $$\frac{2mg_0R^2}{(R+h)}$$ 4 $$-\frac{2mg_0R^2}{(R+h)}$$
Subtopic:  Gravitational Potential Energy |
77%
From NCERT
NEET - 2016
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints