Gravitational Field Due to a Shell

Q. Q. Two spherical raindrops of equal size are falling vertically through air with a terminal velocity of 1m/s. What would be the terminal speed if these two drops were to coalesce to form a larger spherical drop.

Q.

Which one of the following plots represents the variation of gravitational field on a particle with distance r due a thin spherical shell of radius R?

1. 

2. 

3. 

4. 

Q.

The gravitational potential (V) and gravitational field (E) are plotted against distance r from the centre of a uniform spherical shell .Consider the following statement

A)the plot of V against r is discontinuous

B)the plot of E against r is discontinuous

Which statement is correct or wrong and why?

Q. Imagine a geo-stationary satellite of earth which is used as an intercontinental telecast station. At what height will it have to be established

1. ${10}^3\text{m}$
2. $6.4\times {10}^3\text{m}$
3. $35.94\times {10}^6\text{m}$
4. Infinity

Q. A geostationary satellite is orbiting the earth at a height $6R$ above the surface of the earth, where $R$ is the radius of earth. The time period of another satellite revolving around earth at a height $2.5R$ from earth's surface is :

1. $12\sqrt{2}$ hr
2. $12$ hr
3. $6\sqrt{2}$ hr
4. $6$ hr

Q. Satellite is revolving around earth. If its radius of orbit is increased to $4$ times of the radius of geostationary satellite, what will be its time period?

1. $2\text{days}$
2. $8\text{days}$
3. $16\text{days}$
4. $4\text{days}$

Q. By what fraction does the mass of a spring change when it is compressed by 1 cm? The mass of the spring is 200 g at its natural length and the spring constant is 500 N m⁻¹.

Q.

what is the force of attraction between hollow

spherical shell of uniform density on a point

mass inside ?

Q.
The net gravitational field at point $P$ is

1. $\frac{\sqrt{65}}{72}\frac{GM}{R^2}$
2. $\frac{1}{9}\frac{GM}{R^2}$
3. $\frac{\sqrt{3}}{2}\frac{GM}{R^2}$
4. $\frac{\sqrt{65}}{36}\frac{GM}{R^2}$
   

Q. Why is gravitational field intensity zero inside the spherical shell although constant in case of gravitational potential ?

Q. Imagine a geostationary satellite of earth which is used as an inter continental telecast station. At what height will it have to be established $?$$(\text{Take}G=6.67\times {10}^{-11}{\text{Nm}}^2{\text{kg}}^{-2}$ and mass of earth, $M=6\times {10}^{24}\text{kg})$.

1. $6.4\times {10}^3\text{m}$
   
2. $35.94\times {10}^6\text{m}$
   
3. $\infty$
4. ${10}^3\text{m}$
   

Q. A geostationary satellite orbits around the earth in a circular orbit of radius $36000km$. Then, the time period of a spy satellite orbiting a few $100km$ above the earth's surface $R_{earth}=6400km$ will approximately be

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

Q. The gravitational field inside a spherical shell is

1. Towards the center
2. Away from the center
3. Zero
4. Cannot say

Q. A geostationary satellite orbits around the earth in a circular orbit of radius $36000km$. Then, the period of spy satellite orbiting three hundred kilometers above the earth's surface ($R_{earth}=6400km$) will become :

1. $\left(1/2\right)hr$
2. $1.5hr$
3. $2hr$
4. $4hr$

Q. The distance of a geostationary satellite from the centre of earth (radius R = 6400 Km) is nearly.

1. 18 R
2. 10R
3. 7R
4. 5R

Q. If a satellite is revolving around a planet of mass M in an elliptical orbit of semi-major axis a. Show that the orbital speed of the satellite when it is at a distance r from the planet will be given by $V^2=GM[\frac{2}{r}-\frac{1}{a}]$.

Q. a satellite can be in a geostationary orbit around a planet at a distance r from the centre of the planet. If the angular velocity of the planet about its axis doubles, a satellite can now be in a geostationary orbit around the planet if its distance from the centre of the planet is

1. $\frac{r}{2}$
2. $\frac{r}{2\sqrt{2}}$
3. $\frac{r}{(4{)}^{1/3}}$
4. $\frac{r}{(2{)}^{1/3}}$

Q. Satellite is revolving around the earth. If it's radius of orbit is increased to $4$ times the radius of geostationary satellite, what will become its time period ?

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

Q. An artificial satellite is revolving round the earth. The radius of its circular orbit is half the orbital radius of moon. The time taken by this satellite in completing one revolution will be

1. $2$ lunar months.
2. $2^{-2/3}$ lunar months.
3. $1/2$ lunar months.
4. $2^{-3/2}$ lunar months.

Q.

What is the intensity of gravitational field of the centre of a uniform spherical shell

1. Zero

2. None of these

3. 

4. g

Q. An artificial satellite of the earth is launched in a circular orbit in the equatorial plane of the earth and the satellite is moving from west to east. With respect to a person on the equator, the satellite is completing one round trip in 24 h. Mass of the earth is $M=6\times {10}^{24}kg$. For this situation, the orbital radius of the satellite is

1. 6400 km
2. $2.66\times {10}^{4}km$
3. 36, 000 km
4. 29, 600 km

Q. A satellite moving on a circular path of radius $r$ around Earth has a time period $T$. If its radius slightly increases by $\Delta r$, the change in its time period is

1. $\left(\frac{T}{r}\right)\Delta r$
2. $\frac{3}{2}\left(\frac{T}{r}\right)\Delta r$
3. $\frac{3}{2}\left(\frac{T^2}{r^2}\right)\Delta r$
4. none of these

Q. If $R$ is the average radius of earth, $\omega$ is its angular velocity about its axis and $g$ is the gravitational acceleration on the surface of earth then the cube of the radius of orbit of a geostationary satellite will be equal to.

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

Q. The radius of the orbit of a geosynchronous satellite is $36000$ $km$. Then, find the period of revolution of a satellite with its orbital radius $9000$ $km$.

1. $24$ $hrs$
2. $6$ $hrs$
3. $12$ $hrs$
4. $3$ $hrs$

Q. The altitude of a geostationary satellite is nearly $6$ times the radius of the Earth. The period of revolution of an identical satellite revolving at an altitude $0.75$ times the radius of the Earth will be :

1. $4hrs$
2. $3hrs$
3. $12hrs$
4. $2hrs$

Q. The time period of a satellite in a circular orbit of radius $R$ is $T$, the period of another satellite in a circular orbit of radius $4R$ is

1. $4T$
2. $T/4$
3. $8T$
4. $T/8$

Q. Intensity of gravitational field inside hollow uniform spherical shell

1. is zero at center but nonzero at other points.
2. is nonzero at all points.
3. is zero at all points because variables regims of shell attracts point mass in various directions, these forces cancel each other completely.
4. is non uniform & varies linearly.

Q. A satellite orbiting around earth in an orbit of radius $R$ is shifted to an orbit of radius $2R$. Times the time taken for one revolution will become.

1. $8times$
2. $2times$
3. $2.5times$
4. $2.8times$

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 accelaration due to gravity at the surface of the earth. The velocity of the satellite in orbit is given by

1. $g{R}^2/(R+h)$
2. $gR$
3. $gR/(R-h)$
4. $\sqrt{\left[g{R}^2/\right(R+h\left)\right]}$

Q. Geo-stationary satellite revolves at ____________.

1. Any height
2. Fixed height
3. Height above pole
4. Height which depends upon its mass