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) 26th June Morning Shift
Numerical
+4
-1 The elongation of a wire on the surface of the earth is 10$$-$$4 m. The same wire of same dimensions is elongated by 6 $$\times$$ 10$$-$$5 m on another planet. The acceleration due to gravity on the planet will be ____________ ms$$-$$2. (Take acceleration due to gravity on the surface of earth = 10 ms$$-$$2)

3
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 = ___________.

4
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 ____________.
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