1
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket of mass $${m \over {10}}$$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G is the gravitational constant; M is the mass of the earth) :
A
$${{3m} \over 8}{\left( {u + \sqrt {{{5GM} \over {6R}}} } \right)^2}$$
B
$${m \over {20}}\left( {{u^2} + {{113} \over {100}}{{GM} \over R}} \right)$$
C
$$5m\left( {{u^2} - {{119} \over {100}}{{GM} \over R}} \right)$$
D
$${m \over {20}}{\left( {u - \sqrt {{{2GM} \over {3R}}} } \right)^2}$$
2
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass of the planet is $${1 \over 9}$$ th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)
A
$${R \over 9}$$
B
$${R \over 2}$$
C
$${R \over 3}$$
D
$${R \over 4}$$
3
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet?

[Given ; Mass of planet = 8 × 1022 kg, Radius of planet = 2 × 106 m, Gravitational constant G = 6.67 × 10–11 Nm2 /kg2]
A
13
B
9
C
17
D
11
4
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
The value of acceleration due to gravity at Earth's surface is 9.8 ms–2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms–2, is close to : (Radius of earth = 6.4 × 106 m)
A
1.6 × 106 m
B
9.0 × 106 m
C
6.4 × 106 m
D
2.6 × 106 m
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