A planet of mass M, has two natural satellites with masses m 1 a n d m 2 . The radii of their circular orbits are R 1   a n d   R 2 respectively. Ignore the gravitational force between the satellites. Define v 1 , L 1 , K 1   a n d   T 1 to be, respectively, the orbital speed,…

Question

A planet of mass M, has two natural satellites with masses m 1 a n d m 2 . The radii of their circular orbits are R 1 &#160; a n d &#160; R 2 respectively. Ignore the gravitational force between the satellites. Define v 1 , L 1 , K 1 &#160; a n d &#160; T 1 to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1 ; &#160; a n d &#160; v 2 , L 2 , K 2 a n d &#160; T 2 and to be the corresponding quantities of satellite 2. Given m 1 / m 2 = 2 &#160; a n d &#160; R 1 / R 2 = 1 4 , match the ratios in List-I to the numbers in List-II. LIST -I LIST-II A) v 1 v 2 P) 1 8 B) L 1 L 2 Q) 1 C) K 1 K 2 R) 2 D) T 1 T 2 S) 8

Aicharya · Accepted Answer

m 1 m 2 = 2 R 1 R 2 = 1 4 given G M m 1 R 1 2 = m 1 V 1 1 R 1 v 1 2 = G M R 1 , v 2 2 = G M R 2 v 1 2 v 2 2 = R 2 R 1 = 4 i v 1 v 2 = 2 i i L = m v R L 1 L 2 = m 1 v 1 R 1 m 2 v 2 R 2 = 2 × 2 × 1 4 = 1 i i i K = 1 2 m v 2 K 1 K 2 = m 1 v 1 2 m 2 v 2 2 = 2 × 2 2 = 8 ( i v ) T = 2 π R / V T 1 T 2 = R 1 v 1 × v 2 R 2 = R 1 R 2 × v 2 v 1 = 1 4 × 1 2 = 1 8 ;

A planet of mass M, has two natural satellites with masses m 1 a n d m 2 . The radii of their circular…

Solution

	LIST -I		LIST-II
A)	$\frac{v_{1}}{v_{2}}$	P)	$\frac{1}{8}$
B)	$\frac{L_{1}}{L_{2}}$	Q)	1
C)	$\frac{K_{1}}{K_{2}}$	R)	2
D)	$\frac{T_{1}}{T_{2}}$	S)	8