1
JEE Main 2014 (Offline)
+4
-1
Four particles, each of mass $$M$$ and equidistant from each other, move along a circle of radius $$R$$ under the action of their mutual gravitational attraction. The speed of each particle is :
A
$$\sqrt {{{GM} \over R}}$$
B
$$\sqrt {2\sqrt 2 {{GM} \over R}}$$
C
$$\sqrt {{{GM} \over R}\left( {1 + 2\sqrt 2 } \right)}$$
D
$${1 \over 2}\sqrt {{{GM} \over R}\left( {1 + 2\sqrt 2 } \right)}$$
2
JEE Main 2013 (Offline)
+4
-1
What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and radius $$R$$ in a circular orbit at an altitude of $$2R$$?
A
$${{5GmM} \over {6R}}$$
B
$${{2GmM} \over {3R}}$$
C
$${{GmM} \over {2R}}$$
D
$${{GmM} \over {3R}}$$
3
AIEEE 2012
+4
-1
The mass of a spaceship is $$1000$$ $$kg.$$ It is to be launched from the earth's surface out into free space. The value of $$g$$ and $$R$$ (radius of earth ) are $$10\,m/{s^2}$$ and $$6400$$ $$km$$ respectively. The required energy for this work will be:
A
$$6.4 \times {10^{11}}\,$$ Joules
B
$$6.4 \times {10^8}\,$$ Joules
C
$$6.4 \times {10^9}\,$$ Joules
D
$$6.4 \times {10^{10}}\,$$ Joules
4
AIEEE 2011
+4
-1
Two bodies of masses $$m$$ and $$4$$ $$m$$ are placed at a distance $$r.$$ The gravitational potential at a point on the line joining them where the gravitational field is zero is:
A
$$- {{4Gm} \over r}$$
B
$$- {{6Gm} \over r}$$
C
$$- {{9Gm} \over r}$$
D
zero
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