03. Kepler's Law of Planetary Motion
Gravitation

138629 A geo- stationary satellite is orbiting the Earth at a height $7 \mathrm{R}$ from the earth's surface. If the satellite is pulled into a closer orbit which is at a height $R$ from the earths surface, its time period becomes ( $R$ is radius of earth)

1 $3 \mathrm{hrs}$
2 $3 \sqrt{2} \mathrm{hrs}$
3 $6 \sqrt{2} \mathrm{hrs}$
4 $\frac{6}{\sqrt{2}} \mathrm{hrs}$
Gravitation

138630 If a graph is plotted between $T^{2}$ and $r^{3}$ for a planet, then its slope will be

1 $\frac{4 \pi^{2}}{\mathrm{GM}}$
2 $\frac{\mathrm{GM}}{4 \pi^{3}}$
3 $4 \pi \mathrm{GM}$
4 GM
Gravitation

138631 A planet of mass $m$ moves around the Sun along an elliptical path with a period of revolution $T$. During the motion, the planet's maximum and minimum distance from Sun is $R$ and $\frac{R}{3}$ respectively. If $T^{2}=\alpha R^{3}$, then the magnitude of constant $\alpha$ will be

1 $\frac{10}{9} \cdot \frac{\pi}{\mathrm{Gm}}$
2 $\frac{20}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
3 $\frac{32}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
4 $\frac{1}{18} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
Gravitation

138632 A body is orbiting around Earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is-

1 4 days
2 16 days
3 $2 \sqrt{2}$ days
4 64 days
Gravitation

138633 Taking that Earth revolves around the Sun in a circular orbit of radius $15 \times 10^{10} \mathrm{~m}$, with a time period of 1 year. The time taken by another planet, which is at a distance of $540 \times 10^{10} \mathrm{~m}$, to revolve around the Sun in circular orbit once, will be

1 $216 \mathrm{yr}$
2 $144 \mathrm{yr}$
3 $72 \mathrm{yr}$
4 $36 \mathrm{yr}$
Gravitation

138629 A geo- stationary satellite is orbiting the Earth at a height $7 \mathrm{R}$ from the earth's surface. If the satellite is pulled into a closer orbit which is at a height $R$ from the earths surface, its time period becomes ( $R$ is radius of earth)

1 $3 \mathrm{hrs}$
2 $3 \sqrt{2} \mathrm{hrs}$
3 $6 \sqrt{2} \mathrm{hrs}$
4 $\frac{6}{\sqrt{2}} \mathrm{hrs}$
Gravitation

138630 If a graph is plotted between $T^{2}$ and $r^{3}$ for a planet, then its slope will be

1 $\frac{4 \pi^{2}}{\mathrm{GM}}$
2 $\frac{\mathrm{GM}}{4 \pi^{3}}$
3 $4 \pi \mathrm{GM}$
4 GM
Gravitation

138631 A planet of mass $m$ moves around the Sun along an elliptical path with a period of revolution $T$. During the motion, the planet's maximum and minimum distance from Sun is $R$ and $\frac{R}{3}$ respectively. If $T^{2}=\alpha R^{3}$, then the magnitude of constant $\alpha$ will be

1 $\frac{10}{9} \cdot \frac{\pi}{\mathrm{Gm}}$
2 $\frac{20}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
3 $\frac{32}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
4 $\frac{1}{18} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
Gravitation

138632 A body is orbiting around Earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is-

1 4 days
2 16 days
3 $2 \sqrt{2}$ days
4 64 days
Gravitation

138633 Taking that Earth revolves around the Sun in a circular orbit of radius $15 \times 10^{10} \mathrm{~m}$, with a time period of 1 year. The time taken by another planet, which is at a distance of $540 \times 10^{10} \mathrm{~m}$, to revolve around the Sun in circular orbit once, will be

1 $216 \mathrm{yr}$
2 $144 \mathrm{yr}$
3 $72 \mathrm{yr}$
4 $36 \mathrm{yr}$
Gravitation

138629 A geo- stationary satellite is orbiting the Earth at a height $7 \mathrm{R}$ from the earth's surface. If the satellite is pulled into a closer orbit which is at a height $R$ from the earths surface, its time period becomes ( $R$ is radius of earth)

1 $3 \mathrm{hrs}$
2 $3 \sqrt{2} \mathrm{hrs}$
3 $6 \sqrt{2} \mathrm{hrs}$
4 $\frac{6}{\sqrt{2}} \mathrm{hrs}$
Gravitation

138630 If a graph is plotted between $T^{2}$ and $r^{3}$ for a planet, then its slope will be

1 $\frac{4 \pi^{2}}{\mathrm{GM}}$
2 $\frac{\mathrm{GM}}{4 \pi^{3}}$
3 $4 \pi \mathrm{GM}$
4 GM
Gravitation

138631 A planet of mass $m$ moves around the Sun along an elliptical path with a period of revolution $T$. During the motion, the planet's maximum and minimum distance from Sun is $R$ and $\frac{R}{3}$ respectively. If $T^{2}=\alpha R^{3}$, then the magnitude of constant $\alpha$ will be

1 $\frac{10}{9} \cdot \frac{\pi}{\mathrm{Gm}}$
2 $\frac{20}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
3 $\frac{32}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
4 $\frac{1}{18} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
Gravitation

138632 A body is orbiting around Earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is-

1 4 days
2 16 days
3 $2 \sqrt{2}$ days
4 64 days
Gravitation

138633 Taking that Earth revolves around the Sun in a circular orbit of radius $15 \times 10^{10} \mathrm{~m}$, with a time period of 1 year. The time taken by another planet, which is at a distance of $540 \times 10^{10} \mathrm{~m}$, to revolve around the Sun in circular orbit once, will be

1 $216 \mathrm{yr}$
2 $144 \mathrm{yr}$
3 $72 \mathrm{yr}$
4 $36 \mathrm{yr}$
Gravitation

138629 A geo- stationary satellite is orbiting the Earth at a height $7 \mathrm{R}$ from the earth's surface. If the satellite is pulled into a closer orbit which is at a height $R$ from the earths surface, its time period becomes ( $R$ is radius of earth)

1 $3 \mathrm{hrs}$
2 $3 \sqrt{2} \mathrm{hrs}$
3 $6 \sqrt{2} \mathrm{hrs}$
4 $\frac{6}{\sqrt{2}} \mathrm{hrs}$
Gravitation

138630 If a graph is plotted between $T^{2}$ and $r^{3}$ for a planet, then its slope will be

1 $\frac{4 \pi^{2}}{\mathrm{GM}}$
2 $\frac{\mathrm{GM}}{4 \pi^{3}}$
3 $4 \pi \mathrm{GM}$
4 GM
Gravitation

138631 A planet of mass $m$ moves around the Sun along an elliptical path with a period of revolution $T$. During the motion, the planet's maximum and minimum distance from Sun is $R$ and $\frac{R}{3}$ respectively. If $T^{2}=\alpha R^{3}$, then the magnitude of constant $\alpha$ will be

1 $\frac{10}{9} \cdot \frac{\pi}{\mathrm{Gm}}$
2 $\frac{20}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
3 $\frac{32}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
4 $\frac{1}{18} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
Gravitation

138632 A body is orbiting around Earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is-

1 4 days
2 16 days
3 $2 \sqrt{2}$ days
4 64 days
Gravitation

138633 Taking that Earth revolves around the Sun in a circular orbit of radius $15 \times 10^{10} \mathrm{~m}$, with a time period of 1 year. The time taken by another planet, which is at a distance of $540 \times 10^{10} \mathrm{~m}$, to revolve around the Sun in circular orbit once, will be

1 $216 \mathrm{yr}$
2 $144 \mathrm{yr}$
3 $72 \mathrm{yr}$
4 $36 \mathrm{yr}$
Gravitation

138629 A geo- stationary satellite is orbiting the Earth at a height $7 \mathrm{R}$ from the earth's surface. If the satellite is pulled into a closer orbit which is at a height $R$ from the earths surface, its time period becomes ( $R$ is radius of earth)

1 $3 \mathrm{hrs}$
2 $3 \sqrt{2} \mathrm{hrs}$
3 $6 \sqrt{2} \mathrm{hrs}$
4 $\frac{6}{\sqrt{2}} \mathrm{hrs}$
Gravitation

138630 If a graph is plotted between $T^{2}$ and $r^{3}$ for a planet, then its slope will be

1 $\frac{4 \pi^{2}}{\mathrm{GM}}$
2 $\frac{\mathrm{GM}}{4 \pi^{3}}$
3 $4 \pi \mathrm{GM}$
4 GM
Gravitation

138631 A planet of mass $m$ moves around the Sun along an elliptical path with a period of revolution $T$. During the motion, the planet's maximum and minimum distance from Sun is $R$ and $\frac{R}{3}$ respectively. If $T^{2}=\alpha R^{3}$, then the magnitude of constant $\alpha$ will be

1 $\frac{10}{9} \cdot \frac{\pi}{\mathrm{Gm}}$
2 $\frac{20}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
3 $\frac{32}{27} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
4 $\frac{1}{18} \cdot \frac{\pi^{2}}{\mathrm{Gm}}$
Gravitation

138632 A body is orbiting around Earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is-

1 4 days
2 16 days
3 $2 \sqrt{2}$ days
4 64 days
Gravitation

138633 Taking that Earth revolves around the Sun in a circular orbit of radius $15 \times 10^{10} \mathrm{~m}$, with a time period of 1 year. The time taken by another planet, which is at a distance of $540 \times 10^{10} \mathrm{~m}$, to revolve around the Sun in circular orbit once, will be

1 $216 \mathrm{yr}$
2 $144 \mathrm{yr}$
3 $72 \mathrm{yr}$
4 $36 \mathrm{yr}$