Q. Two stars each of one solar mass $(=2\times {10}^{30}kg)$ are approaching each other for a head on collision. When they are a distance ${10}^{9}km$, their speeds are negligible. What is the speed with which they collide ? The radius of each star is ${10}^{4}km$. Assume the stars to remain undistorted until they collide. (Use the known value of G).

Q. One of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is $4.22\times {10}^{8}m$. Show that the mass of Jupiter is about one-thousandth that of the sun.

Q. How will you 'weigh the sun', that is estimate its mass? The mean orbital radius of the earth around the sun is $1.5\times {10}^{8}km$.

Q. A rocket is fired from the earth towards the sun. At what distance from the earths centre is the gravitational force on the rocket zero? Mass of the sun = $2\times {10}^{30}kg$, mass of the earth = $6\times {10}^{24}kg$. Neglect the effect of other planets etc. (orbital radius = $1.5\times {10}^{11}m$).

Q. Choose the correct alternative :
(a) Acceleration due to gravity increases/decreases with increasing altitude.
(b) Acceleration due to gravity increases/decreases with increasing depth (assume the earth to be a sphere of uniform density).
(c) Acceleration due to gravity is independent of mass of the earth/mass of the body.
(d) The formula $-GMm(1/r_2-1/r_1)$ is more/less accurate than the formula $mg(r_2-r_1)$ for the difference of potential energy between two points $r_2$ and $r_1$ distance away from the center of the earth.

Q. Let us assume that our galaxy consists of $2.5\times {10}^{11}$ 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 ? Take the diameter of the Milky Way to be ${10}^5$ ly.

Q. 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 force and potential at the mid point of the line joining the centres of the spheres ? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable ?

Q. As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly 36, 000 km from the surface of the earth. What is the potential due to earth's gravity at the site of this satellite ? (Take the potential energy at infinity to be zero). Mass of the earth = $6.0\times {10}^{24}kg$, radius = 6400 km.

Q. Assuming the earth to be a sphere of uniform mass density, how much would a body weigh (in N) half way down to the center of the earth if it weighed 250 N on the surface ?

Q. A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (a) Linear speed, (b) angular speed, (c) Angular momentum, (d) Kinetic energy, (e) potential energy, (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

Q. The escape speed of a projectile on the earth's surface is $11.2km{s}^{-1}$. 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.

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

Q.

Does the escape speed of a body from the earth depend on

(a) The mass of the body,

(b) The location from where it is projected,

(c) The direction of projection,

(d) The height of the location from where the body is launched?

Q. Answer the following:
(a) You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
(b) An astronaut inside a small space ship orbiting around the earth cannot detect gravity. If the space station orbiting around the earth has a large size, can he hope to detect gravity?
(c) If you compare the gravitational force on the earth due to the sun to that due to the moon, you would find that the Sun's pull is greater than the moon's pull. However, the tidal effect of the moon's pull is greater than the tidal effect of the sun. Why?

Q. A rocket is fired vertically with a speed of $5km{s}^{-1}$ from the Earth's surface. How far from the Earth does the rocket go before returning to the Earth ? Mass of the earth $=6.0\times {10}^{24}kg$; mean radius of the radius of the Earth $=6.4\times {10}^{6}m$; $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$.

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

Q. Which of the following symptoms is not likely to afflict an astronaut in space (a) swollen feet, (b) swollen face, (c) headache, (d) orientational problem.

Q. Choose the correct alternative:
(a) If the zero of potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic / potential energy.
(b) The energy required to launch an orbiting satellite out of earths gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earths influence.

Q. A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is $1.50\times {10}^{8}km$ away from the sun ?

Q. 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 $=200kg$; mass of the earth $=6.0\times {10}^{24}kg$; radius of the earth $=6.4\times {10}^{6}m$; G = $6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$.