1
JEE Main 2015 (Offline)
+4
-1
From a solid sphere of mass $$M$$ and radius $$R,$$ a spherical portion of radius $$R/2$$ is removed, as shown in the figure. Taking gravitational potential $$V=0$$ at $$r = \infty ,$$ the potential at the center of the cavity thus formed is:
($$G=gravitational$$ $$constant$$)
A
$${{ - 2GM} \over {3R}}$$
B
$${{ - 2GM} \over R}$$
C
$${{ - GM} \over {2R}}$$
D
$${{ - GM} \over R}$$
2
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
$${1 \over 2}\sqrt {{{GM} \over R}\left( {1 + 2\sqrt 2 } \right)}$$
3
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
$${{GmM} \over {3R}}$$
4
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
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