03. Kepler's Law of Planetary Motion
Gravitation

138606 The distance of Neptune and Saturn from the sun is nearly $10^{13}$ and $10^{12}$ meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio of

1 10
2 100
3 $10 \sqrt{10}$
4 1000
Gravitation

138609 Kepler's third law states that the square of period of revolution ( $T$ ) of a planet around the sun, is proportional to third power of average distance, $r$ between the sun and the planet i.e. $\mathbf{T}^{2}=\mathrm{Kr}^{3}$
Here, $K$ is constant.
If masses of the sun and the planet are $M$ and $m$ respectively, then as per Newton's law and $m$ respectively, force of attraction between them is $\mathbf{F}=\frac{\mathbf{G M m}}{\mathbf{r}^{2}}$, where $G$ is gravitational constant.
The relation between $G$ and $K$ is described as

1 $\mathrm{GK}=4 \pi^{2}$
2 $\mathrm{GMK}=4 \pi^{2}$
3 $\mathrm{K}=\mathrm{G}$
4 $K=\frac{1}{G}$
Gravitation

138610 A planet moving around the sun sweeps area $A_{1}$ in 2 days, $A_{2}$ in 4 days and $A_{3}$ in 9 days. Then, relation between them.

1 $\mathrm{A}_{1}=\mathrm{A}_{2}=\mathrm{A}_{3}$
2 $9 \mathrm{~A}_{1}=3 \mathrm{~A}_{2}=2 \mathrm{~A}_{3}$
3 $18 \mathrm{~A}_{1}=9 \mathrm{~A}_{2}=4 \mathrm{~A}_{3}$
4 $3 \mathrm{~A}_{1}=4 \mathrm{~A}_{2}=6 \mathrm{~A}_{3}$
Gravitation

138611 Two planets revolves around the sun with frequencies $N_{1}$ and $N_{2}$ revolutions per year. If their average radii (orbital) be $R_{1}$ and $R_{2}$ respectively, then $R_{1} / R_{2}$ is equal to-

1 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{2 / 3}$
2 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{3 / 2}$
3 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{2 / 3}$
4 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{3 / 2}$
Gravitation

138614 The earth takes $24 \mathrm{hr}$ to rotate once about its axis. How much time does the sun take to shift by $5^{\circ}$ when viewed from the earth?

1 $20 \mathrm{~min}$
2 $15 \mathrm{~min}$
3 $10 \mathrm{~min}$
4 $5 \mathrm{~min}$
Gravitation

138606 The distance of Neptune and Saturn from the sun is nearly $10^{13}$ and $10^{12}$ meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio of

1 10
2 100
3 $10 \sqrt{10}$
4 1000
Gravitation

138609 Kepler's third law states that the square of period of revolution ( $T$ ) of a planet around the sun, is proportional to third power of average distance, $r$ between the sun and the planet i.e. $\mathbf{T}^{2}=\mathrm{Kr}^{3}$
Here, $K$ is constant.
If masses of the sun and the planet are $M$ and $m$ respectively, then as per Newton's law and $m$ respectively, force of attraction between them is $\mathbf{F}=\frac{\mathbf{G M m}}{\mathbf{r}^{2}}$, where $G$ is gravitational constant.
The relation between $G$ and $K$ is described as

1 $\mathrm{GK}=4 \pi^{2}$
2 $\mathrm{GMK}=4 \pi^{2}$
3 $\mathrm{K}=\mathrm{G}$
4 $K=\frac{1}{G}$
Gravitation

138610 A planet moving around the sun sweeps area $A_{1}$ in 2 days, $A_{2}$ in 4 days and $A_{3}$ in 9 days. Then, relation between them.

1 $\mathrm{A}_{1}=\mathrm{A}_{2}=\mathrm{A}_{3}$
2 $9 \mathrm{~A}_{1}=3 \mathrm{~A}_{2}=2 \mathrm{~A}_{3}$
3 $18 \mathrm{~A}_{1}=9 \mathrm{~A}_{2}=4 \mathrm{~A}_{3}$
4 $3 \mathrm{~A}_{1}=4 \mathrm{~A}_{2}=6 \mathrm{~A}_{3}$
Gravitation

138611 Two planets revolves around the sun with frequencies $N_{1}$ and $N_{2}$ revolutions per year. If their average radii (orbital) be $R_{1}$ and $R_{2}$ respectively, then $R_{1} / R_{2}$ is equal to-

1 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{2 / 3}$
2 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{3 / 2}$
3 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{2 / 3}$
4 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{3 / 2}$
Gravitation

138614 The earth takes $24 \mathrm{hr}$ to rotate once about its axis. How much time does the sun take to shift by $5^{\circ}$ when viewed from the earth?

1 $20 \mathrm{~min}$
2 $15 \mathrm{~min}$
3 $10 \mathrm{~min}$
4 $5 \mathrm{~min}$
Gravitation

138606 The distance of Neptune and Saturn from the sun is nearly $10^{13}$ and $10^{12}$ meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio of

1 10
2 100
3 $10 \sqrt{10}$
4 1000
Gravitation

138609 Kepler's third law states that the square of period of revolution ( $T$ ) of a planet around the sun, is proportional to third power of average distance, $r$ between the sun and the planet i.e. $\mathbf{T}^{2}=\mathrm{Kr}^{3}$
Here, $K$ is constant.
If masses of the sun and the planet are $M$ and $m$ respectively, then as per Newton's law and $m$ respectively, force of attraction between them is $\mathbf{F}=\frac{\mathbf{G M m}}{\mathbf{r}^{2}}$, where $G$ is gravitational constant.
The relation between $G$ and $K$ is described as

1 $\mathrm{GK}=4 \pi^{2}$
2 $\mathrm{GMK}=4 \pi^{2}$
3 $\mathrm{K}=\mathrm{G}$
4 $K=\frac{1}{G}$
Gravitation

138610 A planet moving around the sun sweeps area $A_{1}$ in 2 days, $A_{2}$ in 4 days and $A_{3}$ in 9 days. Then, relation between them.

1 $\mathrm{A}_{1}=\mathrm{A}_{2}=\mathrm{A}_{3}$
2 $9 \mathrm{~A}_{1}=3 \mathrm{~A}_{2}=2 \mathrm{~A}_{3}$
3 $18 \mathrm{~A}_{1}=9 \mathrm{~A}_{2}=4 \mathrm{~A}_{3}$
4 $3 \mathrm{~A}_{1}=4 \mathrm{~A}_{2}=6 \mathrm{~A}_{3}$
Gravitation

138611 Two planets revolves around the sun with frequencies $N_{1}$ and $N_{2}$ revolutions per year. If their average radii (orbital) be $R_{1}$ and $R_{2}$ respectively, then $R_{1} / R_{2}$ is equal to-

1 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{2 / 3}$
2 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{3 / 2}$
3 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{2 / 3}$
4 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{3 / 2}$
Gravitation

138614 The earth takes $24 \mathrm{hr}$ to rotate once about its axis. How much time does the sun take to shift by $5^{\circ}$ when viewed from the earth?

1 $20 \mathrm{~min}$
2 $15 \mathrm{~min}$
3 $10 \mathrm{~min}$
4 $5 \mathrm{~min}$
Gravitation

138606 The distance of Neptune and Saturn from the sun is nearly $10^{13}$ and $10^{12}$ meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio of

1 10
2 100
3 $10 \sqrt{10}$
4 1000
Gravitation

138609 Kepler's third law states that the square of period of revolution ( $T$ ) of a planet around the sun, is proportional to third power of average distance, $r$ between the sun and the planet i.e. $\mathbf{T}^{2}=\mathrm{Kr}^{3}$
Here, $K$ is constant.
If masses of the sun and the planet are $M$ and $m$ respectively, then as per Newton's law and $m$ respectively, force of attraction between them is $\mathbf{F}=\frac{\mathbf{G M m}}{\mathbf{r}^{2}}$, where $G$ is gravitational constant.
The relation between $G$ and $K$ is described as

1 $\mathrm{GK}=4 \pi^{2}$
2 $\mathrm{GMK}=4 \pi^{2}$
3 $\mathrm{K}=\mathrm{G}$
4 $K=\frac{1}{G}$
Gravitation

138610 A planet moving around the sun sweeps area $A_{1}$ in 2 days, $A_{2}$ in 4 days and $A_{3}$ in 9 days. Then, relation between them.

1 $\mathrm{A}_{1}=\mathrm{A}_{2}=\mathrm{A}_{3}$
2 $9 \mathrm{~A}_{1}=3 \mathrm{~A}_{2}=2 \mathrm{~A}_{3}$
3 $18 \mathrm{~A}_{1}=9 \mathrm{~A}_{2}=4 \mathrm{~A}_{3}$
4 $3 \mathrm{~A}_{1}=4 \mathrm{~A}_{2}=6 \mathrm{~A}_{3}$
Gravitation

138611 Two planets revolves around the sun with frequencies $N_{1}$ and $N_{2}$ revolutions per year. If their average radii (orbital) be $R_{1}$ and $R_{2}$ respectively, then $R_{1} / R_{2}$ is equal to-

1 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{2 / 3}$
2 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{3 / 2}$
3 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{2 / 3}$
4 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{3 / 2}$
Gravitation

138614 The earth takes $24 \mathrm{hr}$ to rotate once about its axis. How much time does the sun take to shift by $5^{\circ}$ when viewed from the earth?

1 $20 \mathrm{~min}$
2 $15 \mathrm{~min}$
3 $10 \mathrm{~min}$
4 $5 \mathrm{~min}$
Gravitation

138606 The distance of Neptune and Saturn from the sun is nearly $10^{13}$ and $10^{12}$ meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio of

1 10
2 100
3 $10 \sqrt{10}$
4 1000
Gravitation

138609 Kepler's third law states that the square of period of revolution ( $T$ ) of a planet around the sun, is proportional to third power of average distance, $r$ between the sun and the planet i.e. $\mathbf{T}^{2}=\mathrm{Kr}^{3}$
Here, $K$ is constant.
If masses of the sun and the planet are $M$ and $m$ respectively, then as per Newton's law and $m$ respectively, force of attraction between them is $\mathbf{F}=\frac{\mathbf{G M m}}{\mathbf{r}^{2}}$, where $G$ is gravitational constant.
The relation between $G$ and $K$ is described as

1 $\mathrm{GK}=4 \pi^{2}$
2 $\mathrm{GMK}=4 \pi^{2}$
3 $\mathrm{K}=\mathrm{G}$
4 $K=\frac{1}{G}$
Gravitation

138610 A planet moving around the sun sweeps area $A_{1}$ in 2 days, $A_{2}$ in 4 days and $A_{3}$ in 9 days. Then, relation between them.

1 $\mathrm{A}_{1}=\mathrm{A}_{2}=\mathrm{A}_{3}$
2 $9 \mathrm{~A}_{1}=3 \mathrm{~A}_{2}=2 \mathrm{~A}_{3}$
3 $18 \mathrm{~A}_{1}=9 \mathrm{~A}_{2}=4 \mathrm{~A}_{3}$
4 $3 \mathrm{~A}_{1}=4 \mathrm{~A}_{2}=6 \mathrm{~A}_{3}$
Gravitation

138611 Two planets revolves around the sun with frequencies $N_{1}$ and $N_{2}$ revolutions per year. If their average radii (orbital) be $R_{1}$ and $R_{2}$ respectively, then $R_{1} / R_{2}$ is equal to-

1 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{2 / 3}$
2 $\left(\mathrm{N}_{1} / \mathrm{N}_{2}\right)^{3 / 2}$
3 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{2 / 3}$
4 $\left(\mathrm{N}_{2} / \mathrm{N}_{1}\right)^{3 / 2}$
Gravitation

138614 The earth takes $24 \mathrm{hr}$ to rotate once about its axis. How much time does the sun take to shift by $5^{\circ}$ when viewed from the earth?

1 $20 \mathrm{~min}$
2 $15 \mathrm{~min}$
3 $10 \mathrm{~min}$
4 $5 \mathrm{~min}$