QNEET-2023-Ph-231: NEET 2023 Physics - Class 11 NEET-2023-Ph-231 Solution: A satellite is orbiting just above the surface of the earth…

For a satellite orbiting just above the surface of the Earth, we can use the formula for the period T of the satellite in terms of the Earth's density d and the gravitational constant G: T = 2 � a 3 G M where a is the semi-major axis of the orbit (which is approximately equal to the Earth's radius R for a satellite orbiting just above the surface) and M is the mass of the Earth. We can express the mass of the Earth M in terms of its density d and volume: M = d V = d _ 4 3 � R 3 Now, substitute this expression for M into the equation for T: T = 2 � a 3 G d _ 4 3 � R 3 Since the satellite is orbiting just above the Earth's surface, we can approximate a � R: T = 2 � R 3 G d _ 4 3 � R 3 Simplify the equation: T = 2 � 1 G d _ 4 3 � Now, square both sides of the equation: T 2 = 4 � 2 1 G d _ 4 3 � Simplify further: T 2 = 3 � G d Thus, the quantity 3 � G d represents T 2 .