The gravitational potential energy of an isolated system of three particles, each of mass $$m$$ placed at three corners of an equilateral triangle of side $$l$$ is:
 1 $$-Gm \over {l}^2$$ 2 $$-Gm^2 \over 2{l}$$ 3 $$-2Gm^2 \over {l}$$ 4 $$-3Gm^2 \over {l}$$
Subtopic: Â Gravitational Potential Energy |
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An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy $$E_0$$. Its potential energy is?
1. $$-E_0$$
2. $$1.5E_0$$
3. $$2E_0$$
4. $$E_0$$
Subtopic: Â Gravitational Potential Energy |
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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: Â Gravitational Potential Energy |
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NEET - 2016
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A body of mass $$m$$ is situated at a distance $$4R_e$$ above the Earth's surface, where $$R_e$$ is the radius of the Earth. What minimum energy should be given to the body so that it may escape?
 1 $$mgR_e$$ 2 $$2mgR_e$$ 3 $$\frac{mgR_e}{5}$$ 4 $$\frac{mgR_e}{16}$$
Subtopic: Â Gravitational Potential Energy |
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Three equal masses $$m$$ are placed at the three vertices of an equilateral triangle of side $$r$$. Work required to double the separation between masses will be:

 1 $$Gm^2\over r$$ 2 $$3Gm^2\over r$$ 3 $${3 \over 2}{Gm^2\over r}$$ 4 None of the above
Subtopic: Â Gravitational Potential Energy |
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If a particle is dropped from a height $$h = 3R$$ from the earth's surface, the speed with which the particle will strike the ground is:
1. $$\sqrt{3gR}$$
2. $$\sqrt{2gR}$$
3. $$\sqrt{1.5gR}$$
4. $$\sqrt{gR}$$

Subtopic: Â Gravitational Potential Energy |
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A rocket of mass $$M$$ is launched vertically from the surface of the earth with an initial speed $$v$$. Assuming the radius of the earth to be $$R$$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is:
1. $$\frac{R}{\left(\frac{gR}{2v^2}-1\right)}$$
2. $$R\left({\frac{gR}{2v^2}-1}\right)$$
3. $$\frac{R}{\left(\frac{2gR}{v^2}-1\right)}$$
4. $$R{\left(\frac{2gR}{v^2}-1\right)}$$

Subtopic: Â Gravitational Potential Energy |
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