1
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
A body weights 49N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?

[Use $$g = {{GM} \over {{R^2}}}$$ = 9.8 ms$$-$$2 and radius of earth, R = 6400 km.]
A
49 N
B
49.83 N
C
48.83 N
D
49.17 N
2
JEE Main 2021 (Online) 24th February Morning Shift
+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
$${1\over2}\sqrt {G(1 + 2\sqrt 2 )}$$
3
JEE Main 2021 (Online) 24th February Morning Shift
+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
4
JEE Main 2021 (Online) 24th February Morning Shift
+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
$$2\pi \sqrt {{{{d^3}} \over {3Gm}}}$$
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