1
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
Inside a uniform spherical shell :

(1) the gravitational field is zero

(2) the gravitational potential is zero

(3) the gravitational field is same everywhere

(4) the gravitational potential is same everywhere

(5) all of the above

Choose the most appropriate answer from the options given below :
A
(1), (3) and (4) only
B
(5) only
C
(1), (2) and (3) only
D
(2), (3) and (4) only
2
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
$${{2G} \over {{R^3}}}$$
3
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
4
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
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