Choose the correct alternative.

Acceleration due to gravity is:

Suppose there existed a planet that went around the sun twice as fast as the earth. Then its orbital size as compared to that of the earth would be:

One of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is 4.22 × ${10}^8$ m. The ratio of the mass of Jupiter and the mass of the sun nearly is:

$$\begin{gathered} \left(1\right) 1000:1 \\ \left(2\right) 1:1000 \\ \left(3\right) 1:1 \\ \left(4\right) 2000:3 \end{gathered}$$

Choose the correct alternative.

Let us assume that our galaxy consists of 2.5 × ${10}^{11}$ stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? (The diameter of the milky way is ${10}^5$ ly.)

$$\begin{gathered} \left(1\right) 3.55\times {10}^8 \mathrm{years} \\ \left(2\right) 4.55\times {10}^8 \mathrm{years} \\ \left(3\right) 3.55\times {10}^7 \mathrm{years} \\ \left(4\right) 4.55\times {10}^7 \mathrm{years} \end{gathered}$$

The escape speed of a body from the earth depends on:

A comet orbits the sun in a highly elliptical orbit. The comet has a constant:

Which of the following symptoms is not likely to afflict an astronaut in space?

The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow: 

Two heavy spheres each of mass 100 kg and radius 0.10 m are placed 1.0 m apart on a horizontal table. What is the gravitational potential at the midpoint of the line joining the centres of the spheres?

$$\begin{gathered} \left(1\right) 2.67\times {10}^{-8} J k{g}^{-1} \\ \left(2\right) 0 \\ \left(3\right) 6.67\times {10}^{-9} J k{g}^{-1} \\ \left(4\right) 3.71\times {10}^{-8} J k{g}^{-1} \end{gathered}$$

A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero?

Given, the mass of the sun = $2\times {10}^{30}$ kg, the mass of the earth =  $6\times {10}^{24}$kg, and orbital radius = $1.5\times {10}^{11}$ m. Neglect the effect of other planets etc.

$$\begin{gathered} \left(1\right) 2.59\times {10}^8 m \\ \left(2\right) 3.10\times {10}^8 m \\ \left(3\right) 4.07\times {10}^8 m \\ \left(4\right) 2.23\times {10}^8 m \end{gathered}$$

If the mean orbital radius of the earth around the sun is $1.5\times {10}^8 km$. Then the mass of the sun is approximately:

$$\begin{gathered} \left(1\right) 3\times {10}^{34} kg \\ \left(2\right) 2\times {10}^{30} kg \\ \left(3\right) 1.5\times {10}^{28} kg \\ \left(4\right) 1.0\times {10}^{35} kg \end{gathered}$$

A Saturn year is 29.5 times the earth year. How far is Saturn from the sun if the earth is $1.5\times {10}^8 km$ away from the sun?

$$\begin{gathered} \left(1\right) 2.01\times {10}^{12} m \\ \left(2\right) 3.86\times {10}^{12} m \\ \left(3\right) 1.43\times {10}^{12} m \\ \left(4\right) 4.19\times {10}^{12} m \end{gathered}$$

A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed 250 N on the surface?

A rocket is fired vertically with a speed of 5 km/s from the earth’s surface. How far from the earth does the rocket go before returning to the earth?

$$\begin{gathered} \left(1\right) 8\times {10}^6 m \\ \left(2\right) 1.6\times {10}^6 m \\ \left(3\right) 6.4\times {10}^6 m \\ \left(4\right) 12\times {10}^6 m \end{gathered}$$

The escape speed of a projectile on the earth’s surface is 11.2 km/s. A body is projected out with thrice this speed. What is the speed of the body far away from the earth?  (Ignore the presence of the sun and other planets.)

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? (Mass of the satellite = 200 kg; mass of the earth = 6.0×${10}^{24}$ kg, radius of the earth = 6.4 × ${10}^6$ m, G = 6.67 × ${10}^{-11}$ $N m^2 k{g}^{-2}$)

$$\begin{gathered} \left(1\right) 7.5\times {10}^9 J \\ \left(2\right) 4.7\times {10}^9 J \\ \left(3\right) 4.4\times {10}^9 J \\ \left(4\right) 5.9\times {10}^9 J \end{gathered}$$

An artificial satellite revolves around a planet for which gravitational force (F) varies with the distance r from its centre as $\mathrm{F}\propto {\mathrm{r}}^2$. If v₀ is its orbital speed, then:

A spaceship is stationed on Mars. How much energy must be expended on the spaceship to launch it out of the solar system? (Mass of the space ship = 1000 kg; mass of the sun = 2×${10}^{30}$ kg; mass of mars = 6.4×${10}^{23}$ kg; radius of mars = 3395 km; radius of the orbit of mars = 2.28×${10}^8$ km; G = 6.67×${10}^{-11}$$N m^2 k{g}^{-2}$.)

$$\begin{gathered} \left(1\right) 11\times {10}^{10} J \\ \left(2\right) 6\times {10}^{11} J \\ \left(3\right) 6.67\times {10}^{10} J \\ \left(4\right) 7.12\times {10}^{11} J \end{gathered}$$

A rocket is fired vertically from the surface of mars with a speed of 2 km/s. If 20% of its initial energy is lost due to martian atmospheric resistance, how far will the rocket go from the surface of Mars before returning to it?

(Mass of mars = 6.4×${10}^{23}$ kg; radius of mars = 3395 km; G = 6.67×${10}^{-11}$ $N m^2 k{g}^{-2}.$)

According to Kepler, the planets move in:

The minimum and maximum distances of a planet revolving around the sun are r and R. If the minimum speed of the planet on its trajectory is v₀, its maximum speed will be:

The torque on a planet about the centre of the sun is:

During the motion of a planet from perihelion to aphelion, the work done by the gravitational force of the sun on it is:

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:

Gravitation is the phenomenon of interaction between:

The Force of gravitation between two masses is found to be F in a vacuum. If both the masses are dipped in water at the same distance, then the new force will be:

The gravitational constant depends upon: