1
JEE Main 2016 (Offline)
+4
-1
A satellite is revolving in a circular orbit at a height $$'h'$$ from the earth's surface (radius of earth $$R;h < < R$$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere.)
A
$$\sqrt{2 g R}$$
B
$$\sqrt{g R}$$
C
$$\sqrt{g R / 2}$$
D
$$\sqrt{g R}(\sqrt{2}-1)$$
2
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
$${{ - GM} \over R}$$
3
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
$${1 \over 2}\sqrt {{{GM} \over R}\left( {1 + 2\sqrt 2 } \right)}$$
4
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
$${{GmM} \over {3R}}$$
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