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**Exercise : ** Solutions of Questions on Page Number : **201**

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Q1 :
**
**

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.
(You can check this yourself using the data available in the
succeeding exercises). However, the tidal effect of the
moon's pull
is greater than the tidal effect of sun. Why?

**Answer :**

**Answer:** (a) No (b) Yes

**(a)** Gravitational influence of matter on nearby objects
cannot be screened by any means. This is because gravitational
force unlike electrical forces is independent of the nature of
the material medium. Also, it is independent of the status of
other objects.

**(b)** If the size of the space station is large enough, then
the astronaut will detect the change in
Earth's
gravity (g).

**(c)** Tidal effect depends inversely upon the cube of the
distance while, gravitational force depends inversely on the
square of the distance. Since the distance between the Moon and
the Earth is smaller than the distance between the Sun and the
Earth, the tidal effect of the
Moon's pull
is greater than the tidal effect of the
Sun's pull.

Answer needs Correction? Click Here

Q2 :
**
**

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 -*G
Mm*(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 centre of the earth.

**Answer :**

**Answer:**

**(a)** Decreases

**(b)** Decreases

**(c)** Mass of the body

**(d)** More

**Explanation:**

**(a)** Acceleration due to gravity at depth *h* is given
by the relation:

Where,

= Radius of the Earth

g = Acceleration due to gravity on the surface of the Earth

It is clear from the given relation that acceleration due to gravity decreases with an increase in height.

**(b)** Acceleration due to gravity at depth *d* is given
by the relation:

It is clear from the given relation that acceleration due to gravity decreases with an increase in depth.

**(c)** Acceleration due to gravity of body of mass *m*
is given by the relation:

Where,

G = Universal gravitational constant

*M* = Mass of the Earth

*R* = Radius of the Earth

Hence, it can be inferred that acceleration due to gravity is independent of the mass of the body.

**(d)** Gravitational potential energy of two points
*r*_{2} and *r*_{1} distance away from
the centre of the Earth is respectively given by:

Hence, this formula is more accurate than the formula
*m*g(*r*_{2}â€“
*r*_{1}).

Answer needs Correction? Click Here

Q3 :
**
**

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?

**Answer :**

Q4 :
**
**

Io, one of the satellites of Jupiter, has an orbital period of
1.769 days and the radius of the orbit is 4.22
x 10^{8} m. Show that
the mass of Jupiter is about one-thousandth that of the sun.

**Answer :**

Q5 :
**
**

Let us assume that our galaxy consists of 2.5
x 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.

**Answer :**

Q6 :
**
**

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.

**Answer :**

Q7 :
**
**

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?

**Answer :**

Q8 :
**
**

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.

**Answer :**

Q9 :
**
**

Which of the following symptoms is likely to afflict an astronaut in space (a) swollen feet, (b) swollen face, (c) headache, (d) orientational problem?

**Answer :**

Q10 :
**
**

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) O.

**Answer :**

Q11 :
**
**

Choose the correct answer from among the given ones:

For the problem 8.10, the direction of the gravitational intensity at an arbitrary point P is indicated by the arrow (i) d, (ii) e, (iii) f, (iv) g.

**Answer :**

Q12 :
**
**

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 x 10^{30} kg,
mass of the earth = 6 x
10^{24} kg. Neglect the effect of other planets etc.
(orbital radius = 1.5 x
10^{11} m).

**Answer :**

Q13 :
**
**

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

**Answer :**

Q14 :
**
**

A Saturn year is 29.5 times the earth year. How far is the Saturn
from the sun if the earth is 1.50
x 10^{8} km away from
the sun?

**Answer :**

Q15 :
**
**

A body weighs 63 N 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?

**Answer :**

Q16 :
**
**

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?

**Answer :**

Q17 :
**
**

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
x 10^{24} kg; mean
radius of the earth = 6.4 x
10^{6} m; G= 6.67 x
10^{-11} N m^{2}
kg^{-}^{2.}

**Answer :**

Q18 :
**
**

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.

**Answer :**

Q19 :
**
**

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
x 10^{24} kg; radius of
the earth = 6.4 x 10^{6}
m; G = 6.67 x
10^{-11} N m^{2}
kg^{-2}.

**Answer :**

Q20 :
**
**

Two stars each of one solar mass (=
2 x 10^{30} kg) are
approaching each other for a head on collision. When they are a
distance 109 km, their speeds are negligible. What is the speed
with which they collide? The radius of each star is 104 km.
Assume the stars to remain undistorted until they collide. (Use
the known value of G).

**Answer :**

Q21 :
**
**

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 centers of the spheres? Is an object placed at that point in equilibrium? If so, is the equilibrium stable or unstable?

**Answer :**

Q22 :
**
**

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
x 10^{24} kg, radius =
6400 km.

**Answer :**

Q23 :
**
**

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 x
10^{30} kg).

**Answer :**

Q24 :
**
**

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

**Answer :**

Q25 :
**
**

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 x 1023 kg; radius of mars =
3395 km; G = 6.67 x
10^{-11} N m^{2}
kg^{-2}.

**Answer :**

Physics Part-1 - Physics : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Gravitation ** will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- Physics Part-1 : Chapter 3 - Motion In A Plane Class 11
- Physics Part-1 : Chapter 1 - Units And Measurements Class 11
- Physics Part-1 : Chapter 2 - Motion In A Straight Line Class 11
- Physics Part-1 : Chapter 4 - Laws Of Motion Class 11
- Physics Part-2 : Chapter 1 - Mechanical Properties Of Solids Class 11
- Physics Part-1 : Chapter 5 - Work, Energy And Power Class 11
- Physics Part-2 : Chapter 7 - Waves Class 11
- Physics Part-1 : Chapter 6 - System Of Particles And Rotational Motion Class 11
- Physics Part-2 : Chapter 4 - Thermodynamics Class 11