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1
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 ___________.
2
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)
3
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 ________.  The initial velocity vi required to project a body vertically upward from the surface of the earth to reach a height of 10R, where R is the radius of the earth, may be described in terms of escape velocity ve such that $${v_i} = \sqrt {{x \over y}} \times {v_e}$$. The value of x will be ____________.