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

138705 If the acceleration due to gravity $g$ doubles and the radius of earth becomes half that of the present value, then the value of escape velocity is (Assume, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ and radius of earth, $R=$ $6400 \mathrm{~km})$

1 $12 \mathrm{~km} / \mathrm{s}$
2 $16 \sqrt{2} \mathrm{~km} / \mathrm{s}$
3 $8 \sqrt{2} \mathrm{~km} / \mathrm{s}$
4 $4 \sqrt{2} \mathrm{~km} / \mathrm{s}$
Gravitation

138706 If a satellite has to orbit the earth in a circular path every $6 \mathrm{hrs}$, at what distance from the surface of the earth should be satellite placed (radius of earth, $R_{e}=6400 \mathrm{~km}$ ) (Assume, $\frac{G M}{4 \pi^{2}}=8.0 \times 10^{12} \mathrm{~N} / \mathrm{m}^{2} \mathrm{~kg}$, where, $G$ and $M$ are gravitational constant and mass of earth and $10^{1 / 3}=2.1$.

1 $15100 \mathrm{~km}$
2 $8720 \mathrm{~km}$
3 $20600 \mathrm{~km}$
4 $5560 \mathrm{~km}$
Gravitation

138707 A stationary object is released from a point $P$ a distance $3 R$ from the centre of the moon which has radius $R$ and mass $M$. Which one of the following expressions gives the speed of the object on hitting the moon?

1 $\left(\frac{2 \mathrm{GM}}{3 \mathrm{R}}\right)^{\frac{1}{2}}$
2 $\left(\frac{4 \mathrm{GM}}{3 \mathrm{R}}\right)^{\frac{1}{2}}$
3 $\left(\frac{2 \mathrm{GM}}{\mathrm{R}}\right)^{\frac{1}{2}}$
4 $\left(\frac{\mathrm{GM}}{\mathrm{R}}\right)^{\frac{1}{2}}$
Gravitation

138709 The mass of the moon is $\frac{1}{81}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that

1 The radius of earth is $\frac{9}{\sqrt{6}}$ of the moon
2 the radius of moon is $\frac{81}{6}$ of the earth
3 moon is the satellite of the earth
4 None of the above
Gravitation

138705 If the acceleration due to gravity $g$ doubles and the radius of earth becomes half that of the present value, then the value of escape velocity is (Assume, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ and radius of earth, $R=$ $6400 \mathrm{~km})$

1 $12 \mathrm{~km} / \mathrm{s}$
2 $16 \sqrt{2} \mathrm{~km} / \mathrm{s}$
3 $8 \sqrt{2} \mathrm{~km} / \mathrm{s}$
4 $4 \sqrt{2} \mathrm{~km} / \mathrm{s}$
Gravitation

138706 If a satellite has to orbit the earth in a circular path every $6 \mathrm{hrs}$, at what distance from the surface of the earth should be satellite placed (radius of earth, $R_{e}=6400 \mathrm{~km}$ ) (Assume, $\frac{G M}{4 \pi^{2}}=8.0 \times 10^{12} \mathrm{~N} / \mathrm{m}^{2} \mathrm{~kg}$, where, $G$ and $M$ are gravitational constant and mass of earth and $10^{1 / 3}=2.1$.

1 $15100 \mathrm{~km}$
2 $8720 \mathrm{~km}$
3 $20600 \mathrm{~km}$
4 $5560 \mathrm{~km}$
Gravitation

138707 A stationary object is released from a point $P$ a distance $3 R$ from the centre of the moon which has radius $R$ and mass $M$. Which one of the following expressions gives the speed of the object on hitting the moon?

1 $\left(\frac{2 \mathrm{GM}}{3 \mathrm{R}}\right)^{\frac{1}{2}}$
2 $\left(\frac{4 \mathrm{GM}}{3 \mathrm{R}}\right)^{\frac{1}{2}}$
3 $\left(\frac{2 \mathrm{GM}}{\mathrm{R}}\right)^{\frac{1}{2}}$
4 $\left(\frac{\mathrm{GM}}{\mathrm{R}}\right)^{\frac{1}{2}}$
Gravitation

138709 The mass of the moon is $\frac{1}{81}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that

1 The radius of earth is $\frac{9}{\sqrt{6}}$ of the moon
2 the radius of moon is $\frac{81}{6}$ of the earth
3 moon is the satellite of the earth
4 None of the above
Gravitation

138705 If the acceleration due to gravity $g$ doubles and the radius of earth becomes half that of the present value, then the value of escape velocity is (Assume, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ and radius of earth, $R=$ $6400 \mathrm{~km})$

1 $12 \mathrm{~km} / \mathrm{s}$
2 $16 \sqrt{2} \mathrm{~km} / \mathrm{s}$
3 $8 \sqrt{2} \mathrm{~km} / \mathrm{s}$
4 $4 \sqrt{2} \mathrm{~km} / \mathrm{s}$
Gravitation

138706 If a satellite has to orbit the earth in a circular path every $6 \mathrm{hrs}$, at what distance from the surface of the earth should be satellite placed (radius of earth, $R_{e}=6400 \mathrm{~km}$ ) (Assume, $\frac{G M}{4 \pi^{2}}=8.0 \times 10^{12} \mathrm{~N} / \mathrm{m}^{2} \mathrm{~kg}$, where, $G$ and $M$ are gravitational constant and mass of earth and $10^{1 / 3}=2.1$.

1 $15100 \mathrm{~km}$
2 $8720 \mathrm{~km}$
3 $20600 \mathrm{~km}$
4 $5560 \mathrm{~km}$
Gravitation

138707 A stationary object is released from a point $P$ a distance $3 R$ from the centre of the moon which has radius $R$ and mass $M$. Which one of the following expressions gives the speed of the object on hitting the moon?

1 $\left(\frac{2 \mathrm{GM}}{3 \mathrm{R}}\right)^{\frac{1}{2}}$
2 $\left(\frac{4 \mathrm{GM}}{3 \mathrm{R}}\right)^{\frac{1}{2}}$
3 $\left(\frac{2 \mathrm{GM}}{\mathrm{R}}\right)^{\frac{1}{2}}$
4 $\left(\frac{\mathrm{GM}}{\mathrm{R}}\right)^{\frac{1}{2}}$
Gravitation

138709 The mass of the moon is $\frac{1}{81}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that

1 The radius of earth is $\frac{9}{\sqrt{6}}$ of the moon
2 the radius of moon is $\frac{81}{6}$ of the earth
3 moon is the satellite of the earth
4 None of the above
Gravitation

138705 If the acceleration due to gravity $g$ doubles and the radius of earth becomes half that of the present value, then the value of escape velocity is (Assume, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ and radius of earth, $R=$ $6400 \mathrm{~km})$

1 $12 \mathrm{~km} / \mathrm{s}$
2 $16 \sqrt{2} \mathrm{~km} / \mathrm{s}$
3 $8 \sqrt{2} \mathrm{~km} / \mathrm{s}$
4 $4 \sqrt{2} \mathrm{~km} / \mathrm{s}$
Gravitation

138706 If a satellite has to orbit the earth in a circular path every $6 \mathrm{hrs}$, at what distance from the surface of the earth should be satellite placed (radius of earth, $R_{e}=6400 \mathrm{~km}$ ) (Assume, $\frac{G M}{4 \pi^{2}}=8.0 \times 10^{12} \mathrm{~N} / \mathrm{m}^{2} \mathrm{~kg}$, where, $G$ and $M$ are gravitational constant and mass of earth and $10^{1 / 3}=2.1$.

1 $15100 \mathrm{~km}$
2 $8720 \mathrm{~km}$
3 $20600 \mathrm{~km}$
4 $5560 \mathrm{~km}$
Gravitation

138707 A stationary object is released from a point $P$ a distance $3 R$ from the centre of the moon which has radius $R$ and mass $M$. Which one of the following expressions gives the speed of the object on hitting the moon?

1 $\left(\frac{2 \mathrm{GM}}{3 \mathrm{R}}\right)^{\frac{1}{2}}$
2 $\left(\frac{4 \mathrm{GM}}{3 \mathrm{R}}\right)^{\frac{1}{2}}$
3 $\left(\frac{2 \mathrm{GM}}{\mathrm{R}}\right)^{\frac{1}{2}}$
4 $\left(\frac{\mathrm{GM}}{\mathrm{R}}\right)^{\frac{1}{2}}$
Gravitation

138709 The mass of the moon is $\frac{1}{81}$ of the earth but the gravitational pull is $\frac{1}{6}$ of the earth. It is due to the fact that

1 The radius of earth is $\frac{9}{\sqrt{6}}$ of the moon
2 the radius of moon is $\frac{81}{6}$ of the earth
3 moon is the satellite of the earth
4 None of the above