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 = 2×1030 kg,
mass of the earth = 6×1024 kg. Neglect the effect of other planets etc. (orbital radius
= 1.5 × 1011 m)
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.
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 7.11) (i) a, (ii) b, (iii) c, (iv) 0.
Which of the following symptoms is likely to afflict an astronaut in space (a) swollen
feet, (b) swollen face, (c) headache, (d) orientational problem.
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.
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?
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.
Let us assume that our galaxy consists of 2.5 × 1011 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 105
ly.
Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius
of the orbit is 4.22 × 108
m. Show that the mass of Jupiter is about one-thousandth
that of the sun.
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