1
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is :
A
$$\sqrt {{G \over {2{R^3}}}}$$
B
$${1 \over 2}\sqrt {{G \over {{R^3}}}}$$
C
$${1 \over {2R}}\sqrt {{1 \over G}}$$
D
$${{2G} \over {{R^3}}}$$
2
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 $$\times$$ 103 km. Find the mass of Mars.

$$\left\{ {Given\,{{4{\pi ^2}} \over G} = 6 \times {{10}^{11}}{N^{ - 1}}{m^{ - 2}}k{g^2}} \right\}$$
A
5.96 $$\times$$ 1019 kg
B
3.25 $$\times$$ 1021 kg
C
7.02 $$\times$$ 1025 kg
D
6.00 $$\times$$ 1023 kg
3
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :
A
2W
B
W
C
$${2^{{1 \over 3}}}$$W
D
$$\sqrt 2$$W
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
The minimum and maximum distances of a planet revolving around the sun are x1 and x2. If the minimum speed of the planet on its trajectory is v0 then its maximum speed will be :
A
$${{{v_0}x_1^2} \over {x_2^2}}$$
B
$${{{v_0}x_2^2} \over {x_1^2}}$$
C
$${{{v_0}x_1^{}} \over {x_2^{}}}$$
D
$${{{v_0}x_2^{}} \over {x_1^{}}}$$
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