Q: 8.25 A rocket is fired ‘vertically’ from the surface of mars with a speed of . If 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 ; radius of mars ; .
Q: 8.24 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 ; mass of the sun ; mass of mars ; radius of mars;radius of the orbit of mars ;
Q: 8.23 A star times the mass of the sun and collapsed to a size of rotates with a speed of 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 ).
Q: 8.22 As you have learnt in the text, a geostationary satellite orbits the earth at a height of nearly 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 , radius .
Q: 8.20 Two stars each of one solar mass () are approaching each other for a head on collision. When they are a distance , their speeds are negligible. What is the speed with which they collide? The radius of each star is . Assume the stars to remain undistorted until they collide. (Use the known value of G).
Q: 8.19 A satellite orbits the earth at a height of above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? Mass of the satellite ; ! mass of the earth ; radius of the earth ; .
Q: 8.18 The escape speed of a projectile on the earth’s surface is . 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: 8.17 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 ; mean radius of the earth ; .
Q: 8.16 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 on the surface?
Q: 8.15 A body weighs 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?
Q: 8.14 A saturn year is times the earth year. How far is the saturn from the sun if the earth is away from the sun?
Q: 8.13 How will you ‘weigh the sun’, that is estimate its mass? The mean orbital radius of the earth around the sun is .
Q: 8.12 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 , mass of the earth . Neglect the effect of other planets etc. (orbital radius ).
Q: 8.11 For the above problem, the direction of the gravitational intensity at an arbitrary point P is indicated by the arrow (i) d, (ii) e, (iii) f, (iv) g.
Q: 8.10 In the following two exercises, 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) (i) a, (ii) b, (iii) c, (iv) 0
Q: 8.9 Which of the following symptoms is likely to afflict an astronaut in space (a) swollen feet, (b) swollen face, (c) headache, (d) orientational problem.
Q: 8.8 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: 8.7 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: 8.6 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 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.
Q: 8.5 Let us assume that our galaxy consists of stars each of one solar mass. How long will a star at a distance of ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be ly.