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

138710 A mass of $6 \times 10^{24} \mathrm{~kg}$ is to be compressed in a sphere in such a way that the escape velocity from the sphere is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$. What should be the radius of the sphere?
$\left(G=6.67 \times 10^{-11} \mathrm{~N}-\mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

1 $9 \mathrm{~km}$
2 $9 \mathrm{~m}$
3 $9 \mathrm{~cm}$
4 $9 \mathrm{~mm}$
Gravitation

138711 A satellite in a circular orbit of radius $R$ has a period of $4 \mathrm{~h}$. Another satellite with orbital radius $3 R$ around the same planet with have a period (in hours)

1 16
2 4
3 $4 \sqrt{27}$
4 $4 \sqrt{8}$
Gravitation

138712 For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

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

138713 A body is projected vertical upwards from the surface of a planet of radius $r$ with a velocity equal to $1 / 3$ rd the escape velocity for the planet. The maximum height attained by the body is :

1 $R / 2$
2 $R / 3$
3 $\mathrm{R} / 5$
4 $\mathrm{R} / 9$
Gravitation

138710 A mass of $6 \times 10^{24} \mathrm{~kg}$ is to be compressed in a sphere in such a way that the escape velocity from the sphere is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$. What should be the radius of the sphere?
$\left(G=6.67 \times 10^{-11} \mathrm{~N}-\mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

1 $9 \mathrm{~km}$
2 $9 \mathrm{~m}$
3 $9 \mathrm{~cm}$
4 $9 \mathrm{~mm}$
Gravitation

138711 A satellite in a circular orbit of radius $R$ has a period of $4 \mathrm{~h}$. Another satellite with orbital radius $3 R$ around the same planet with have a period (in hours)

1 16
2 4
3 $4 \sqrt{27}$
4 $4 \sqrt{8}$
Gravitation

138712 For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

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

138713 A body is projected vertical upwards from the surface of a planet of radius $r$ with a velocity equal to $1 / 3$ rd the escape velocity for the planet. The maximum height attained by the body is :

1 $R / 2$
2 $R / 3$
3 $\mathrm{R} / 5$
4 $\mathrm{R} / 9$
Gravitation

138710 A mass of $6 \times 10^{24} \mathrm{~kg}$ is to be compressed in a sphere in such a way that the escape velocity from the sphere is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$. What should be the radius of the sphere?
$\left(G=6.67 \times 10^{-11} \mathrm{~N}-\mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

1 $9 \mathrm{~km}$
2 $9 \mathrm{~m}$
3 $9 \mathrm{~cm}$
4 $9 \mathrm{~mm}$
Gravitation

138711 A satellite in a circular orbit of radius $R$ has a period of $4 \mathrm{~h}$. Another satellite with orbital radius $3 R$ around the same planet with have a period (in hours)

1 16
2 4
3 $4 \sqrt{27}$
4 $4 \sqrt{8}$
Gravitation

138712 For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

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

138713 A body is projected vertical upwards from the surface of a planet of radius $r$ with a velocity equal to $1 / 3$ rd the escape velocity for the planet. The maximum height attained by the body is :

1 $R / 2$
2 $R / 3$
3 $\mathrm{R} / 5$
4 $\mathrm{R} / 9$
Gravitation

138710 A mass of $6 \times 10^{24} \mathrm{~kg}$ is to be compressed in a sphere in such a way that the escape velocity from the sphere is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$. What should be the radius of the sphere?
$\left(G=6.67 \times 10^{-11} \mathrm{~N}-\mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

1 $9 \mathrm{~km}$
2 $9 \mathrm{~m}$
3 $9 \mathrm{~cm}$
4 $9 \mathrm{~mm}$
Gravitation

138711 A satellite in a circular orbit of radius $R$ has a period of $4 \mathrm{~h}$. Another satellite with orbital radius $3 R$ around the same planet with have a period (in hours)

1 16
2 4
3 $4 \sqrt{27}$
4 $4 \sqrt{8}$
Gravitation

138712 For a satellite moving in an orbit around the earth, the ratio of kinetic energy to potential energy is

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

138713 A body is projected vertical upwards from the surface of a planet of radius $r$ with a velocity equal to $1 / 3$ rd the escape velocity for the planet. The maximum height attained by the body is :

1 $R / 2$
2 $R / 3$
3 $\mathrm{R} / 5$
4 $\mathrm{R} / 9$