1
JEE Main 2022 (Online) 29th July Morning Shift
Numerical
+4
-1

If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $$\alpha \mathrm{h}\left(\mathrm{h}<<\mathrm{R}_{\mathrm{e}}\right)$$ from the earth surface. The value of $$\alpha$$ will be _________.

(use $$\left.\mathrm{R}_{\mathrm{e}}=6400 \mathrm{~km}\right)$$

2
JEE Main 2022 (Online) 25th June Evening Shift
Numerical
+4
-1

Two satellites S1 and S2 are revolving in circular orbits around a planet with radius R1 = 3200 km and R2 = 800 km respectively. The ratio of speed of satellite S1 to be speed of satellite S2 in their respective orbits would be $${1 \over x}$$ where x = ___________.

3
JEE Main 2021 (Online) 1st September Evening Shift
Numerical
+4
-1
Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is 2 $$\times$$ 103 km. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $${\pi \over x}rad\,{h^{ - 1}}$$ where x is ____________.
4
JEE Main 2021 (Online) 27th August Morning Shift
Numerical
+4
-1
A body of mass (2M) splits into four masses (m, M $$-$$ m, m, M $$-$$ m}, which are rearranged to form a square as shown in the figure. The ratio of $${M \over m}$$ for which, the gravitational potential energy of the system becomes maximum is x : 1. The value of x is ............ .