Three equal mass satellites $A, B,$ and $C$ are in coplanar orbits around a planet as shown in the figure. The magnitudes of the angular momenta of the satellites as measured about the planet are $L_A, L_B$, and $L_C$. Which of the following statements is correct?
Three equal mass satellites $A, B,$ and $C$ are in coplanar orbits around a planet as shown in the figure. The magnitudes of the angular momenta of the satellites as measured about the planet are $L_A, L_B$, and $L_C$. Which of the following statements is correct?
- A
$L_A > L_B > L_C$
- B
$L_C > L_B > L_A$
- C
$L_B > L_C > L_A$
- D
$L_B > L_A > L_C$
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Match List$-I$ With List$-II$
$(a)$ Gravitational constant $(G)$
$(i)$ $\left[ L ^{2} T ^{-2}\right]$
$(b)$ Gravitational potential energy
$(ii)$ $\left[ M ^{-1} L ^{3} T ^{-2}\right]$
$(c)$ Gravitational potential
$(iii)$ $\left[ LT ^{-2}\right]$
$(d)$ Gravitational intensity
$(iv)$ $\left[ ML ^{2} T ^{-2}\right]$
Choose the correct answer from the options given below:
Match List$-I$ With List$-II$
| $(a)$ Gravitational constant $(G)$ | $(i)$ $\left[ L ^{2} T ^{-2}\right]$ |
| $(b)$ Gravitational potential energy | $(ii)$ $\left[ M ^{-1} L ^{3} T ^{-2}\right]$ |
| $(c)$ Gravitational potential | $(iii)$ $\left[ LT ^{-2}\right]$ |
| $(d)$ Gravitational intensity | $(iv)$ $\left[ ML ^{2} T ^{-2}\right]$ |
Choose the correct answer from the options given below:
- [NEET 2022]
Kepler's third law states that square of period of revolution $(T)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet i.e.
$\therefore \;{T^2} = k{r^3}$
here $K$ is constant.
If the masses of sun and planet are $M$ and $m$ respectively then as per Newton's law of gravitation force of attraction between them is $F = \frac{{GMm}}{{{r^2}}}$ , here $G$ gravitational constant . The relation between $G$ and $K$ is described as
Kepler's third law states that square of period of revolution $(T)$ of a planet around the sun, is proportional to third power of average distance $r$ between sun and planet i.e.
$\therefore \;{T^2} = k{r^3}$
here $K$ is constant.
If the masses of sun and planet are $M$ and $m$ respectively then as per Newton's law of gravitation force of attraction between them is $F = \frac{{GMm}}{{{r^2}}}$ , here $G$ gravitational constant . The relation between $G$ and $K$ is described as
- [AIPMT 2015]