Which of the following symptoms is likely to afflict an astronaut in space (a) swollen feet,

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 ?

A rocket is fired vertically with a speed of 5 km 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 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 (a) linear speed, throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

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 = $2 \times 10^{30}$ kg; mass of mars = $6.4 \times 10^{23}$ kg; radius of mars = 3395 km; radius of the orbit of mars = $2.28 \times 10^8$ km; G = $6.67 \times 10^{-11}$ N m$^2$ kg$^{–2}$.

Which of the following symptoms is likely to afflict an astronaut in space (d) orientational problem.

A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity ? (mass of the sun = $2 \times 10^{30}$ kg).

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 answer from among the given ones: The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12)

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.

Choose the correct answer from among the given ones: The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow (see Fig 8.12), the direction of the gravitational intensity at an arbitrary point P is indicated by the arrow.

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$^{–2}$.

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.

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).

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.

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 ?

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

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$^{–2}$.

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