Introduction to Gravitation : Kepler's Laws

Q.

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance$(R/2)$from the earths centre, where$R$ is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:

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

2. $\left(\frac{1}{2\pi }\right)\sqrt{\frac{g}{R}}$

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

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

Q.

Two planets have masses $M$ and $16M$and their radii are $a$ and $2a$, respectively. The separation between the centres of the planets is $10a$. A body of mass $m$ is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach the surface of the smaller planet, the minimum firing speed needed is:

1. $2\sqrt{\frac{GM}{a}}$

2. $\sqrt{\frac{G{M}^2}{ma}}$

3. $\frac{3}{2}\sqrt{\frac{5GM}{a}}$

4. $4\sqrt{\frac{GM}{a}}$

Q.

The planets revolve around the sun in an elliptical path known as ___________.

Q.

The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

Q.

A suitable unit for gravitational constant is

1. $kg-m{s}^{-1}$

2. $N{m}^{-1}s$

3. $N{m}^{2}k{g}^{-2}$

4. $kgm{s}^{-1}$

Q.

What is the actual shape of the orbit of a planet around the sun? What assumption was made by Newton regarding the shape of an orbit of a planet around the sun for deriving his inverse square rule from Kepler's third law of planetary motion?

Q. What is the shape of the path of a planet around the Sun?

1. Parabola
2. Square
3. Ellipse
4. Circle

Q. Explain Newton's Laws of Motion with an example.

Q.

What is Newtons law of gravitation? Define $G$.

Q.

Why do all objects have a tendency to fall towards the earth when thrown up?

Q.

Who invented the gravitation?

Q.

The period of a planet around sun is $27$ times that of the earth. The ratio of radius of planets orbit to the radius of the earths orbit is

1. $4$

2. $9$

3. $64$

4. $27$

Q.

What are Keplers three laws?

Q. A satellite revolves around the earth in an elliptic orbit. Its speed

1. Is the same at all points of the orbit
2. Is the greatest when it is closest to the earth
3. Is the greatest when it is farthest from the earth
4. Depends upon mass of the satellite

Q. Question 15
An apple falls from a tree because of gravitational attraction between the earth and apple. If $F_1$ is the magnitude of force exerted by the earth on the apple and $F_2$ is the magnitude of force exerted by apple on earth, then

(a) $F_1$ is very much greater than $F_2$
(b) $F_2$ is very much greater than $F_1$
(c) $F_1$ is only a little greater than $F_2$
(d) $F_1$ and $F_2$ are equal

Q.

Why weight is given as mass x gravity?

Q.

Newton's third law says that every action has an equal and opposite reaction.this means that the force applied by sun on Earth and by Earth on sun will be equal.then why does sun does not revolve around Earth?why Earth revolves around sun?

Q.

Name the scientist who explained the motion of planets on the basis of gravitational force between the sun and planets.

Q.

According to one of the Kepler's laws of planetary motion :
(a) $r^2\propto T^3$
(b) $r\propto T^2$
(c) $r^3\propto T^2$
(d) $r^3\propto \frac{1}{T^2}$

Q.

Name the scientist who gave the three laws of planetary motion.

Q.

The weight of a body can not be zero.

1. True
2. False

Q.

___________velocity of the planet is constant when it revolves in an elliptical orbit around the sun.

Q. State the Kepler's laws of planetary motion.

Q.

On what factors does the value of gravitational force depend.

Q.

How is the force of attraction dependent on the masses of objects and distance between them?

Q.

State the Kepler's law which is represented by the relation $r^3\propto T^2$.

Q.

Does the Mass affect the Escape Velocity ?

Q.

Who discovered trigonometry?

Q. Which of the following are correct about Kepler's law?

1. The path of the planets around the sun is elliptical, with the sun being located at one of the two foci.
   
2. The line joining the planet and the sun sweeps equal areas in equal intervals of time.
   
3. The cube of the average distance of a planet from the sun is directly proportional to the square of the planet's orbital time period.
   
4. The path of the planets around the sun is circular, with the sun being located at its centre.

Q.

Calculate the force of gravitation between two object of masses 80 kg and 120 kg kept at a distance of 10 m of each other.