04. Escape Velocity, Orbital Velocity, Satellites Motion, Binding Energy
Gravitation

138680 A satellite moves in elliptical orbit about a planet. Its maximum and minimum velocities of satellites are $3 \times 10^{4} \mathrm{~m} / \mathrm{s}$ and $1 \times 10^{3} \mathrm{~m} / \mathrm{s}$ respectively. What is the minimum distance of satellite from planet is maximum distance if $4 \times 10^{4} \mathrm{~km}$ ?

1 $4 \times 10^{3} \mathrm{~km}$
2 $3 \times 10^{3} \mathrm{~km}$
3 $4 / 3 \times 10^{3} \mathrm{~km}$
4 $1 \times 10^{3} \mathrm{~km}$
Gravitation

138681 An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. The height of the satellite above the earth's surface will be

1 $6000 \mathrm{~km}$
2 $5800 \mathrm{~km}$
3 $7500 \mathrm{~km}$
4 $6400 \mathrm{~km}$
Gravitation

138682 A satellite moves round the earth in a circular orbit of radius $R$ making 1 rev/day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is :

1 $8 \mathrm{R}$
2 $4 \mathrm{R}$
3 $2 \mathrm{R}$
4 $\mathrm{R}$
Gravitation

138684 A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at point $A$ and $B$ are $90 \times$ $10^{6} \mathrm{~km}$ and $60 \times 10^{6} \mathrm{~km}$, respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angle $30^{\circ}$ and $60^{\circ}$ with major-axis of the orbit is

1 $\frac{3}{2 \sqrt{3}}$
2 $\frac{2}{\sqrt{3}}$
3 $\frac{1}{\sqrt{3}}$
4 $\frac{\sqrt{3}}{2}$
Gravitation

138685 An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to

1 $\mathrm{m}$
2 $\mathrm{m}^{-1}$
3 $\mathrm{m}^{0}$
4 $\mathrm{m}^{1-2}$
Gravitation

138680 A satellite moves in elliptical orbit about a planet. Its maximum and minimum velocities of satellites are $3 \times 10^{4} \mathrm{~m} / \mathrm{s}$ and $1 \times 10^{3} \mathrm{~m} / \mathrm{s}$ respectively. What is the minimum distance of satellite from planet is maximum distance if $4 \times 10^{4} \mathrm{~km}$ ?

1 $4 \times 10^{3} \mathrm{~km}$
2 $3 \times 10^{3} \mathrm{~km}$
3 $4 / 3 \times 10^{3} \mathrm{~km}$
4 $1 \times 10^{3} \mathrm{~km}$
Gravitation

138681 An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. The height of the satellite above the earth's surface will be

1 $6000 \mathrm{~km}$
2 $5800 \mathrm{~km}$
3 $7500 \mathrm{~km}$
4 $6400 \mathrm{~km}$
Gravitation

138682 A satellite moves round the earth in a circular orbit of radius $R$ making 1 rev/day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is :

1 $8 \mathrm{R}$
2 $4 \mathrm{R}$
3 $2 \mathrm{R}$
4 $\mathrm{R}$
Gravitation

138684 A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at point $A$ and $B$ are $90 \times$ $10^{6} \mathrm{~km}$ and $60 \times 10^{6} \mathrm{~km}$, respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angle $30^{\circ}$ and $60^{\circ}$ with major-axis of the orbit is

1 $\frac{3}{2 \sqrt{3}}$
2 $\frac{2}{\sqrt{3}}$
3 $\frac{1}{\sqrt{3}}$
4 $\frac{\sqrt{3}}{2}$
Gravitation

138685 An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to

1 $\mathrm{m}$
2 $\mathrm{m}^{-1}$
3 $\mathrm{m}^{0}$
4 $\mathrm{m}^{1-2}$
Gravitation

138680 A satellite moves in elliptical orbit about a planet. Its maximum and minimum velocities of satellites are $3 \times 10^{4} \mathrm{~m} / \mathrm{s}$ and $1 \times 10^{3} \mathrm{~m} / \mathrm{s}$ respectively. What is the minimum distance of satellite from planet is maximum distance if $4 \times 10^{4} \mathrm{~km}$ ?

1 $4 \times 10^{3} \mathrm{~km}$
2 $3 \times 10^{3} \mathrm{~km}$
3 $4 / 3 \times 10^{3} \mathrm{~km}$
4 $1 \times 10^{3} \mathrm{~km}$
Gravitation

138681 An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. The height of the satellite above the earth's surface will be

1 $6000 \mathrm{~km}$
2 $5800 \mathrm{~km}$
3 $7500 \mathrm{~km}$
4 $6400 \mathrm{~km}$
Gravitation

138682 A satellite moves round the earth in a circular orbit of radius $R$ making 1 rev/day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is :

1 $8 \mathrm{R}$
2 $4 \mathrm{R}$
3 $2 \mathrm{R}$
4 $\mathrm{R}$
Gravitation

138684 A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at point $A$ and $B$ are $90 \times$ $10^{6} \mathrm{~km}$ and $60 \times 10^{6} \mathrm{~km}$, respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angle $30^{\circ}$ and $60^{\circ}$ with major-axis of the orbit is

1 $\frac{3}{2 \sqrt{3}}$
2 $\frac{2}{\sqrt{3}}$
3 $\frac{1}{\sqrt{3}}$
4 $\frac{\sqrt{3}}{2}$
Gravitation

138685 An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to

1 $\mathrm{m}$
2 $\mathrm{m}^{-1}$
3 $\mathrm{m}^{0}$
4 $\mathrm{m}^{1-2}$
Gravitation

138680 A satellite moves in elliptical orbit about a planet. Its maximum and minimum velocities of satellites are $3 \times 10^{4} \mathrm{~m} / \mathrm{s}$ and $1 \times 10^{3} \mathrm{~m} / \mathrm{s}$ respectively. What is the minimum distance of satellite from planet is maximum distance if $4 \times 10^{4} \mathrm{~km}$ ?

1 $4 \times 10^{3} \mathrm{~km}$
2 $3 \times 10^{3} \mathrm{~km}$
3 $4 / 3 \times 10^{3} \mathrm{~km}$
4 $1 \times 10^{3} \mathrm{~km}$
Gravitation

138681 An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. The height of the satellite above the earth's surface will be

1 $6000 \mathrm{~km}$
2 $5800 \mathrm{~km}$
3 $7500 \mathrm{~km}$
4 $6400 \mathrm{~km}$
Gravitation

138682 A satellite moves round the earth in a circular orbit of radius $R$ making 1 rev/day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is :

1 $8 \mathrm{R}$
2 $4 \mathrm{R}$
3 $2 \mathrm{R}$
4 $\mathrm{R}$
Gravitation

138684 A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at point $A$ and $B$ are $90 \times$ $10^{6} \mathrm{~km}$ and $60 \times 10^{6} \mathrm{~km}$, respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angle $30^{\circ}$ and $60^{\circ}$ with major-axis of the orbit is

1 $\frac{3}{2 \sqrt{3}}$
2 $\frac{2}{\sqrt{3}}$
3 $\frac{1}{\sqrt{3}}$
4 $\frac{\sqrt{3}}{2}$
Gravitation

138685 An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to

1 $\mathrm{m}$
2 $\mathrm{m}^{-1}$
3 $\mathrm{m}^{0}$
4 $\mathrm{m}^{1-2}$
Gravitation

138680 A satellite moves in elliptical orbit about a planet. Its maximum and minimum velocities of satellites are $3 \times 10^{4} \mathrm{~m} / \mathrm{s}$ and $1 \times 10^{3} \mathrm{~m} / \mathrm{s}$ respectively. What is the minimum distance of satellite from planet is maximum distance if $4 \times 10^{4} \mathrm{~km}$ ?

1 $4 \times 10^{3} \mathrm{~km}$
2 $3 \times 10^{3} \mathrm{~km}$
3 $4 / 3 \times 10^{3} \mathrm{~km}$
4 $1 \times 10^{3} \mathrm{~km}$
Gravitation

138681 An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. The height of the satellite above the earth's surface will be

1 $6000 \mathrm{~km}$
2 $5800 \mathrm{~km}$
3 $7500 \mathrm{~km}$
4 $6400 \mathrm{~km}$
Gravitation

138682 A satellite moves round the earth in a circular orbit of radius $R$ making 1 rev/day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is :

1 $8 \mathrm{R}$
2 $4 \mathrm{R}$
3 $2 \mathrm{R}$
4 $\mathrm{R}$
Gravitation

138684 A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at point $A$ and $B$ are $90 \times$ $10^{6} \mathrm{~km}$ and $60 \times 10^{6} \mathrm{~km}$, respectively. The ratio of velocities of the planet at the points $A$ and $B$ when its velocities make angle $30^{\circ}$ and $60^{\circ}$ with major-axis of the orbit is

1 $\frac{3}{2 \sqrt{3}}$
2 $\frac{2}{\sqrt{3}}$
3 $\frac{1}{\sqrt{3}}$
4 $\frac{\sqrt{3}}{2}$
Gravitation

138685 An artificial satellite of mass $m$ is moving along an elliptical path around the earth. The areal velocity of the satellite is proportional to

1 $\mathrm{m}$
2 $\mathrm{m}^{-1}$
3 $\mathrm{m}^{0}$
4 $\mathrm{m}^{1-2}$