1
JEE Main 2021 (Online) 27th July Morning Shift
Numerical
+4
-1
Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is $$\sqrt {{a \over 7}{{GM} \over R}}$$ then the value of 'a' is ____________.

[Given : The two planets are fixed in their position]

2
JEE Main 2021 (Online) 17th March Morning Shift
Numerical
+4
-1
The radius in kilometer to which the present radius of earth (R = 6400 km) to be compressed so that the escape velocity is increased 10 times is ___________.
3
JEE Main 2021 (Online) 16th March Evening Shift
Numerical
+4
-1
If one wants to remove all the mass of the earth to infinity in order to break it up completely.

The amount of energy that needs to be supplied will be $${x \over 5}{{G{M^2}} \over R}$$ where x is __________ (Round off to the Nearest Integer) (M is the mass of earth, R is the radius of earth, G is the gravitational constant)
4
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
In the reported figure of earth, the value of acceleration due to gravity is same at point A and C but it is smaller than that of its value at point B (surface of the earth). The value of OA : AB will be x : y. The value of x is ________.