03. Kepler's Law of Planetary Motion
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Gravitation

138640 A planet of mass ' $m$ ' moves in an elliptical orbit around an unknown star of mass ' $M$ ' such that its maximum and minimum distances from the star are equal to $r_{1}$ and $r_{2}$ respectively. The angular momentum of the planet relative to the centre of the star is

1 $\mathrm{m} \sqrt{\frac{2 \mathrm{GMr}_{1} \mathrm{r}_{2}}{\mathrm{r}_{1}+\mathrm{r}_{2}}}$
2 0
3 $\mathrm{m} \sqrt{\frac{2 \mathrm{GM}\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)}{\mathrm{r}_{1} \mathrm{r}_{2}}}$
4 $\mathrm{m} \sqrt{\frac{2 \mathrm{GMmr}_{1}}{\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right) \mathrm{r}_{2}}}$
Gravitation

138641 A light planet is revolving around a massive star with a period of revolution $T$. If the gravitational force of attraction varies as $\mathbf{r}^{-5 / 2}$, then $T^{2}$ is proportional to ( $r$ is the distance between the planet and star)

1 $\mathrm{r}^{3 / 2}$
2 $r^{5 / 2}$
3 $\mathrm{r}^{7 / 2}$
4 $r^{1 / 2}$
Gravitation

138642 Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A}=2 T_{B}$. These planets are revolving in the circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which out of the following would be the correct relationship of their orbits ?

1 $2 \mathrm{r}_{\mathrm{A}}^{2}=\mathrm{r}_{\mathrm{B}}^{3}$
2 $\mathrm{r}_{\mathrm{A}}^{3}=2 \mathrm{r}_{\mathrm{B}}^{3}$
3 $\mathrm{r}_{\mathrm{A}}^{3}=4 \mathrm{r}_{\mathrm{B}}^{3}$
4 $\mathrm{T}_{\mathrm{A}}^{2}-\mathrm{T}_{\mathrm{B}}^{2}=\frac{\mathrm{r}^{2}}{\mathrm{GM}}\left(\mathrm{r}_{\mathrm{B}}^{3}-4 \mathrm{r}_{\mathrm{A}}^{3}\right)$
Gravitation

138643 The distance of the Sun from Earth is $1.5 \times 10^{11}$ $m$ and its angular diameter is (2000) $s$ when observed from the Earth. The diameter of the Sun will be :

1 $2.45 \times 10^{10} \mathrm{~m}$
2 $1.45 \times 10^{10} \mathrm{~m}$
3 $1.45 \times 10^{9} \mathrm{~m}$
4 $0.14 \times 10^{9} \mathrm{~m}$
Gravitation

138640 A planet of mass ' $m$ ' moves in an elliptical orbit around an unknown star of mass ' $M$ ' such that its maximum and minimum distances from the star are equal to $r_{1}$ and $r_{2}$ respectively. The angular momentum of the planet relative to the centre of the star is

1 $\mathrm{m} \sqrt{\frac{2 \mathrm{GMr}_{1} \mathrm{r}_{2}}{\mathrm{r}_{1}+\mathrm{r}_{2}}}$
2 0
3 $\mathrm{m} \sqrt{\frac{2 \mathrm{GM}\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)}{\mathrm{r}_{1} \mathrm{r}_{2}}}$
4 $\mathrm{m} \sqrt{\frac{2 \mathrm{GMmr}_{1}}{\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right) \mathrm{r}_{2}}}$
Gravitation

138641 A light planet is revolving around a massive star with a period of revolution $T$. If the gravitational force of attraction varies as $\mathbf{r}^{-5 / 2}$, then $T^{2}$ is proportional to ( $r$ is the distance between the planet and star)

1 $\mathrm{r}^{3 / 2}$
2 $r^{5 / 2}$
3 $\mathrm{r}^{7 / 2}$
4 $r^{1 / 2}$
Gravitation

138642 Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A}=2 T_{B}$. These planets are revolving in the circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which out of the following would be the correct relationship of their orbits ?

1 $2 \mathrm{r}_{\mathrm{A}}^{2}=\mathrm{r}_{\mathrm{B}}^{3}$
2 $\mathrm{r}_{\mathrm{A}}^{3}=2 \mathrm{r}_{\mathrm{B}}^{3}$
3 $\mathrm{r}_{\mathrm{A}}^{3}=4 \mathrm{r}_{\mathrm{B}}^{3}$
4 $\mathrm{T}_{\mathrm{A}}^{2}-\mathrm{T}_{\mathrm{B}}^{2}=\frac{\mathrm{r}^{2}}{\mathrm{GM}}\left(\mathrm{r}_{\mathrm{B}}^{3}-4 \mathrm{r}_{\mathrm{A}}^{3}\right)$
Gravitation

138643 The distance of the Sun from Earth is $1.5 \times 10^{11}$ $m$ and its angular diameter is (2000) $s$ when observed from the Earth. The diameter of the Sun will be :

1 $2.45 \times 10^{10} \mathrm{~m}$
2 $1.45 \times 10^{10} \mathrm{~m}$
3 $1.45 \times 10^{9} \mathrm{~m}$
4 $0.14 \times 10^{9} \mathrm{~m}$
Gravitation

138640 A planet of mass ' $m$ ' moves in an elliptical orbit around an unknown star of mass ' $M$ ' such that its maximum and minimum distances from the star are equal to $r_{1}$ and $r_{2}$ respectively. The angular momentum of the planet relative to the centre of the star is

1 $\mathrm{m} \sqrt{\frac{2 \mathrm{GMr}_{1} \mathrm{r}_{2}}{\mathrm{r}_{1}+\mathrm{r}_{2}}}$
2 0
3 $\mathrm{m} \sqrt{\frac{2 \mathrm{GM}\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)}{\mathrm{r}_{1} \mathrm{r}_{2}}}$
4 $\mathrm{m} \sqrt{\frac{2 \mathrm{GMmr}_{1}}{\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right) \mathrm{r}_{2}}}$
Gravitation

138641 A light planet is revolving around a massive star with a period of revolution $T$. If the gravitational force of attraction varies as $\mathbf{r}^{-5 / 2}$, then $T^{2}$ is proportional to ( $r$ is the distance between the planet and star)

1 $\mathrm{r}^{3 / 2}$
2 $r^{5 / 2}$
3 $\mathrm{r}^{7 / 2}$
4 $r^{1 / 2}$
Gravitation

138642 Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A}=2 T_{B}$. These planets are revolving in the circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which out of the following would be the correct relationship of their orbits ?

1 $2 \mathrm{r}_{\mathrm{A}}^{2}=\mathrm{r}_{\mathrm{B}}^{3}$
2 $\mathrm{r}_{\mathrm{A}}^{3}=2 \mathrm{r}_{\mathrm{B}}^{3}$
3 $\mathrm{r}_{\mathrm{A}}^{3}=4 \mathrm{r}_{\mathrm{B}}^{3}$
4 $\mathrm{T}_{\mathrm{A}}^{2}-\mathrm{T}_{\mathrm{B}}^{2}=\frac{\mathrm{r}^{2}}{\mathrm{GM}}\left(\mathrm{r}_{\mathrm{B}}^{3}-4 \mathrm{r}_{\mathrm{A}}^{3}\right)$
Gravitation

138643 The distance of the Sun from Earth is $1.5 \times 10^{11}$ $m$ and its angular diameter is (2000) $s$ when observed from the Earth. The diameter of the Sun will be :

1 $2.45 \times 10^{10} \mathrm{~m}$
2 $1.45 \times 10^{10} \mathrm{~m}$
3 $1.45 \times 10^{9} \mathrm{~m}$
4 $0.14 \times 10^{9} \mathrm{~m}$
Gravitation

138640 A planet of mass ' $m$ ' moves in an elliptical orbit around an unknown star of mass ' $M$ ' such that its maximum and minimum distances from the star are equal to $r_{1}$ and $r_{2}$ respectively. The angular momentum of the planet relative to the centre of the star is

1 $\mathrm{m} \sqrt{\frac{2 \mathrm{GMr}_{1} \mathrm{r}_{2}}{\mathrm{r}_{1}+\mathrm{r}_{2}}}$
2 0
3 $\mathrm{m} \sqrt{\frac{2 \mathrm{GM}\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right)}{\mathrm{r}_{1} \mathrm{r}_{2}}}$
4 $\mathrm{m} \sqrt{\frac{2 \mathrm{GMmr}_{1}}{\left(\mathrm{r}_{1}+\mathrm{r}_{2}\right) \mathrm{r}_{2}}}$
Gravitation

138641 A light planet is revolving around a massive star with a period of revolution $T$. If the gravitational force of attraction varies as $\mathbf{r}^{-5 / 2}$, then $T^{2}$ is proportional to ( $r$ is the distance between the planet and star)

1 $\mathrm{r}^{3 / 2}$
2 $r^{5 / 2}$
3 $\mathrm{r}^{7 / 2}$
4 $r^{1 / 2}$
Gravitation

138642 Two planets $A$ and $B$ of equal mass are having their period of revolutions $T_{A}$ and $T_{B}$ such that $T_{A}=2 T_{B}$. These planets are revolving in the circular orbits of radii $r_{A}$ and $r_{B}$ respectively. Which out of the following would be the correct relationship of their orbits ?

1 $2 \mathrm{r}_{\mathrm{A}}^{2}=\mathrm{r}_{\mathrm{B}}^{3}$
2 $\mathrm{r}_{\mathrm{A}}^{3}=2 \mathrm{r}_{\mathrm{B}}^{3}$
3 $\mathrm{r}_{\mathrm{A}}^{3}=4 \mathrm{r}_{\mathrm{B}}^{3}$
4 $\mathrm{T}_{\mathrm{A}}^{2}-\mathrm{T}_{\mathrm{B}}^{2}=\frac{\mathrm{r}^{2}}{\mathrm{GM}}\left(\mathrm{r}_{\mathrm{B}}^{3}-4 \mathrm{r}_{\mathrm{A}}^{3}\right)$
Gravitation

138643 The distance of the Sun from Earth is $1.5 \times 10^{11}$ $m$ and its angular diameter is (2000) $s$ when observed from the Earth. The diameter of the Sun will be :

1 $2.45 \times 10^{10} \mathrm{~m}$
2 $1.45 \times 10^{10} \mathrm{~m}$
3 $1.45 \times 10^{9} \mathrm{~m}$
4 $0.14 \times 10^{9} \mathrm{~m}$