A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s$^{–1}$. 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 = $6.4 \times 10^{23}$ kg; radius of mars = 3395 km; G = $6.67 \times 10^{-11}$ N m$^2$ kg$^{–2}$.

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 ?

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 ? 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).

Choose the correct alternative: (b) The energy required to launch an orbiting satellite out of earth’s gravitational influence is more/less than the energy required to project a stationary object at the same height (as the satellite) out of earth’s influence.

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (c) angular momentum, throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

Does the escape speed of a body from the earth depend on (a) the mass of the body,

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.

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).

Choose the correct alternative : (c) Acceleration due to gravity is independent of mass of the earth/mass of the body.

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (d) kinetic energy, throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

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 = $6.0 \times 10^{24}$ kg; radius of the earth = $6.4 \times 10^6$ m; G = $6.67 \times 10^{–11}$ N m$^2$ kg$^{–2}$.

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (e) potential energy, throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

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.

Choose the correct alternative : (d) The formula $-G Mm(\frac{1}{r_2} – \frac{1}{r_1})$ 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 centre of the earth.

The escape speed of a projectile on the earth’s surface is 11.2 km 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.

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant (a) linear speed, throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

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

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 ?

Does the escape speed of a body from the earth depend on (d) the height of the location from where the body is launched?