1
JEE Main 2021 (Online) 24th February Morning Slot
+4
-1
Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be :
A
$$\sqrt {{G \over 2}(1 + 2\sqrt 2 )}$$
B
$$\sqrt {{G \over 2}(2\sqrt 2 - 1)}$$
C
$$\sqrt {G(1 + 2\sqrt 2 )}$$
D
$${1\over2}\sqrt {G(1 + 2\sqrt 2 )}$$
2
JEE Main 2021 (Online) 24th February Morning Slot
+4
-1
Consider two satellites S1 and S2 with periods of revolution 1 hr. and 8 hr. respectively revolving around a planet in circular orbits. The ratio of angular velocity of satellite S1 to the angular velocity of satellite S2 is :
A
1 : 4
B
8 : 1
C
2 : 1
D
1 : 8
3
JEE Main 2021 (Online) 24th February Morning Slot
+4
-1
Two stars of masses m and 2m at a distance d rotate about their common centre of mass in free space. The period of revolution is :
A
$${1 \over {2\pi }}\sqrt {{{{d^3}} \over {3Gm}}}$$
B
$$2\pi \sqrt {{{3Gm} \over {{d^3}}}}$$
C
$${1 \over {2\pi }}\sqrt {{{3Gm} \over {{d^3}}}}$$
D
$$2\pi \sqrt {{{{d^3}} \over {3Gm}}}$$
4
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
Two planets have masses M and 16 M and their radii are $$a$$ and 2$$a$$, respectively. The separation between the centres of the planets is 10$$a$$. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is :
A
$$2\sqrt {{{GM} \over a}}$$
B
$$\sqrt {{{G{M^2}} \over {ma}}}$$
C
$${3 \over 2}\sqrt {{{5GM} \over a}}$$
D
$$4\sqrt {{{GM} \over a}}$$
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