Satellites

Q. A satellite of mass $1000kg$ is rotating around the earth in a circular orbit of radius $3R$. What extra energy should be given to this satellite, if it is to be lifted into an orbit of radius $4R$?

1. $6.4\times {10}^{9}J$
2. $4.8\times {10}^{9}J$
3. $2.7\times {10}^{9}J$
4. $3.9\times {10}^{9}J$

Q. The weight of an astronaut, in an artificial satellite revolving around the earth, is

1. Zero
2. Equal to that on the earth
3. More than that on the earth
4. Less than that on the earth

Q.

A satellite is revolving round the earth in circular orbit at some height above surface of earth. It takes $5.26\times {10}^3$ seconds to complete a revolution while its centripetal acceleration is $9.92m/s^2$ . Height of satellite above surface of earth is (Radius of earth $6.37\times {10}^6$ m)

1. 70 km

2. 120 km

3. 170 km

4. 220 km

Q. The orbital velocity of a satellite at point $B$ with radius $r_B$ is $v$. The radius of point $A$ is $r_A$.When satellite is at $A$, the orbit is increased in radial distances uniformly, so that $r_A$ becomes $1.2r_A$ , find the orbital velocity at $\left(1.2r_A\right)$

1. $\frac{v{r}_B}{r_A\sqrt{1.2}}$
2. $\frac{v{r}_A}{1.2r_B}$
3. $\frac{v{r}_B}{1.2r_A}$
4. $\frac{v{r}_A}{r_B\sqrt{1.2}}$

Q.

A geostationary satellite is orbiting the earth at a height of 6R above the surface of the earth; R being the radius of the earth. What will be the time period of another satellite at a height 2.5 R from the surface of the earth?

1. $6\sqrt{2}$ hours

2. $6\sqrt{2.5}$ hours

3. $6\sqrt{3}$ hours

4. $12$ hours

Q.

Select the correct statement from the following

1. The orbital velocity of a satellite increases with the radius of the orbit

2. Escape velocity of a particle from the surface of the earth depends on the speed with which it is fired

3. The time period of a satellite does not depend on the radius of the orbit

4. The orbital velocity is inversely proportional to the square root of the radius of the orbit

Q. For the moon to cease to remain the earth's satellite, its orbital velocity has to increase by a factor of

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

Q. A satellite of mass $1000kg$ is rotating around the earth in a circular orbit of radius $3R$. What extra energy should be given to this satellite, if it is to be lifted into an orbit of radius $4R$?

1. $6.4\times {10}^{9}J$
2. $4.8\times {10}^{9}J$
3. $2.7\times {10}^{9}J$
4. $3.9\times {10}^{9}J$

Q. Chandrayan is a satellite of earth to locate Vikram Lander on the Moon. It is shifted from one stable orbit to another larger and stable orbit. Which of the following quantity increases due to this change?

1. Gravitational potential energy
2. Angular speed
3. Linear orbital speed
4. Centipetal acceleration

Q.

A geostationary satellite orbits around the earth in a circular orbit of radius 36, 000 km. Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface ($R_e$ = 6400 km) will approximately be

1. $\frac{1}{2}$h

2. 1 h

3. 2 h

4. 4 h

Q. The time period of a simple pendulum on a freely moving artificial satellite is

1. Zero
2. 2 sec
3. 3 sec
4. Infinite

Q.

Potential energy of a satellite having mass ‘m’ and rotating at a height of $6.4\times {10}^6$ from the earth centre is

1. $-0.5mg{R}_e$

2. $-mg{R}_e$

3. $-2mg{R}_e$

4. $4mg{R}_e$

Q.

A satellite is moving around the with speed v in a circular orbit of radius r. If the orbit radius is decreased by $1\%$, its speed will

1. $Increaseby1\%$

2. $Increaseby0.5\%$

3. $Decreaseby1\%$

4. $Decreaseby0.5\%$

Q.

A satellite in a force free space sweeps stationary interplanetary dust at a rate $\frac{dM}{dt}=\alpha v$, where M is the mass and v is the velocity of the satellite and $\alpha$ is a constant. The acceleration of the satellite is

1. $-\frac{2\alpha v}{M}$

2. $-\frac{\alpha v^2}{M}$

3. $+\frac{\alpha v^2}{M}$

4. $-\alpha v^2$

Q. A uniform solid sphere of mass $M$ and radius a is surrounded summetrically by a uniform thin spherical shell of equal mass and radius $2\text{a}$. What will be the gravitational field at a distance $\frac{5}{2}$ a from the centre?

1. $\frac{4}{9}\frac{GM}{a^2}$
2. $\frac{8}{25}\frac{GM}{a^2}$
3. $\frac{4}{16}\frac{GM}{a^2}$
4. Zero

Q.

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth :

1. The acceleration of S always directed towards the centre of the earth

2. The angular momentum of S about the cente of the earth changes in direction, but its magnitude remain constant

3. The total mechanical energy of S varies periodically with time

4. The linear momentum of S remains constant in magnitude

Q.

An earth satellite of mass m revolves in a circular orbit at a height h from the surface of the earth. R is the radius of the earth and g is acceleration due to gravity at the surface of the earth. The velocity of the satellite in the orbit is given by

1. $\frac{g{R}^2}{R+h}$

2. gR

3. $\frac{gR}{R+h}$

4. $\sqrt{\frac{g{R}^2}{R+h}}$

Q. An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy $E_0$. Its potential energy is

1. $-E_0$
2. $1.5E_0$
3. $2E_0$
4. $E_0$

Q.

A satellite is revolving round the earth in circular orbit at some height above surface of earth. It takes $5.26\times {10}^3$ seconds to complete a revolution while its centripetal acceleration is $9.92m/s^2$ . Height of satellite above surface of earth is (Radius of earth $6.37\times {10}^6$ m)

1. 70 km

2. 120 km

3. 170 km

4. 220 km

Q.

If G is the universal gravitational constant and $\rho$ is the uniform density of a spherical planet. Then shortest possible period of rotation around a planet can be

1. $\sqrt{\frac{\pi G}{2\rho }}$

2. $\sqrt{\frac{3\pi G}{\rho }}$

3. $\sqrt{\frac{\pi }{6G\rho }}$

4. $\sqrt{\frac{3\pi }{G\rho }}$

Q. Time period of a satellite revolving above Earth’s surface at a height equal to R, where R the radius of Earth, is

1. $4\pi \sqrt{\frac{R}{g}}$
2. $4\pi \sqrt{\frac{2R}{g}}$
3. $8\pi \sqrt{\frac{R}{g}}$
4. $8\pi \sqrt{\frac{2R}{g}}$

Q. A satellite of mass $1000\text{kg}$ is rotating around the earth in a circular orbit of radius $3R$. What extra energy should be given to this satellite if it is to be lifted into an orbit of radius $4R$ ?

1. $6\times {10}^8\text{J}$
2. $3\times {10}^8\text{J}$
3. $2.614\times {10}^9\text{J}$
4. $5.3\times {10}^9\text{J}$

Q. An earth satellite $S$ has an orbit radius which is $4$ times that of a communication satellite $C$. The period of revolution of $S$ is

1. 4 days
2. 8 days
3. 16 days
4. 32 days

Q.

A satellite is moving around the with speed v in a circular orbit of radius r. If the orbit radius is decreased by $1\%$, its speed will

1. $Increaseby1\%$

2. $Increaseby0.5\%$

3. $Decreaseby1\%$

4. $Decreaseby0.5\%$

Q. A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth $(\text{mass}=6\times {10}^{24}\text{kg})$ have to be compressed to be a black hole?

1. ${10}^{-2}\text{m}$
2. $100\text{m}$
3. ${10}^{-9}\text{m}$
4. ${10}^{-6}\text{m}$

Q. The mean radius of the earth is R, its angular speed on its own axis is $\omega$ and the acceleration due to gravity at earth's surface is g. The cube of the radius of the orbit of a geostationary satellite will be

1. $\frac{R^{2}g}{\omega }$
2. $\frac{R^2{\omega }^2}{g}$
3. $\frac{Rg}{{\omega }^2}$
4. $\frac{R^{2}g}{{\omega }^2}$

Q. A spacecraft travels from earth to moon & then on return trip from moon to earth. From earth to moon it requires $f_1$ units of fuel & from moon to earth it requires $f_2$ units of fuel, then

1. $f_1<f_2$
2. $f_1>f_2$
3. $f_1=f_2$
4. Cannot say as it depends upon mass of the space craft

Q.

Periodic time of a satellite revolving above Earth’s surface at a height equal to R, where R the radius of Earth, is [g is acceleration due to gravity at Earth’s surface]

1. $2\pi \sqrt{\frac{2R}{g}}$

2. $4\sqrt{2}\pi \sqrt{\frac{R}{g}}$

3. $2\pi \sqrt{\frac{R}{g}}$

4. $8\pi \sqrt{\frac{R}{g}}$

Q. The total mechanical energy of an object of mass $m$ projected from surface of earth with escape speed is

1. $$-\frac{GMm}{3R}$$
   
2. $-\frac{GMm}{2R}$
   
3. Zero
4. Infinite

Q.

A satellite in a force free space sweeps stationary interplanetary dust at a rate $\frac{dM}{dt}=\alpha v$, where M is the mass and v is the velocity of the satellite and $\alpha$ is a constant. The acceleration of the satellite is

1. $-\frac{2\alpha v}{M}$

2. $-\frac{\alpha v^2}{M}$

3. $+\frac{\alpha v^2}{M}$

4. $-\alpha v^2$