NCERT Solutions Class 11 Physics Chapter 8 Gravitation Download In Pdf

Chapter 8 Gravitation Download in pdf

**Question 8.1** 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 Sunâ€™s pull is greater than the moonâ€™s pull.
(you can check this yourself using the data available in the succeeding exercises).
However, the tidal effect of the moonâ€™s pull is greater than the tidal effect of sun.
Why ?

**Question 8.2** 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 â€“G Mm(1/r2 â€“ 1/r1) is more/less accurate than the formula
mg(r2 â€“ r1) for the difference of potential energy between two points r2 and r1 distance
away from the centre of the earth.

**Question 8.3** 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 ?

**Question 8.4** Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius
of the orbit is 4.22 Ã— 108 m. Show that the mass of Jupiter is about one-thousandth
that of the sun.

**Question 8.5** Let us assume that our galaxy consists of 2.5 Ã— 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.

**Question 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 earthâ€™s gravitational
influence is more/less than the energy required to project a stationary object at
the same height (as the satellite) out of earthâ€™s influence.

**Question 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?

**Question 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.

**Question 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.
In the following two exercises, choose the correct answer from among the given ones:

**Question 8.10** 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

**Question 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.

**Question 8.12** A rocket is fired from the earth towards the sun. At what distance from the earthâ€™s
centre is the gravitational force on the rocket zero ? Mass of the sun = 2Ã— 1030 kg,
mass of the earth = 6Ã— 1024 kg. Neglect the effect of other planets etc. (orbital radius
= 1.5 Ã— 1011 m).

**Question 8.13 **How will you â€˜weigh the sunâ€™, that is estimate its mass? The mean orbital radius of
the earth around the sun is 1.5 Ã— 108 km.

**Question 8.14 **A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the
earth is 1.50 Ã— 108 km away from the sun ?

**Question 8.15** 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 ?

**Question 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 250 N on the surface ?

**Question 8.17** A rocket is fired vertically with a speed of 5 km s-1 from the earthâ€™s surface. How far
from the earth does the rocket go before returning to the earth ? Mass of the earth
= 6.0 Ã— 1024 kg; mean radius of the earth = 6.4 Ã— 106 m; G = 6.67 Ã— 10â€“11 N m2 kgâ€“2.

.**Question 8.18** The escape speed of a projectile on the earthâ€™s surface is 11.2 km sâ€“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.

**Question 8.19** 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 earthâ€™s gravitational
influence? Mass of the satellite = 200 kg; mass of the earth = 6.0Ã— 1024 kg; radius of
the earth = 6.4 Ã— 106 m; G = 6.67 Ã— 10â€“11 N m2 kgâ€“2.

**Question 8.20** Two stars each of one solar mass (= 2Ã— 1030 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).

**Question 8.21** 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 centres of the spheres ? Is an object placed at that point in
equilibrium? If so, is the equilibrium stable or unstable ?
Additional Exercises

**Question 8.22** 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 earthâ€™s
gravity at the site of this satellite ? (Take the potential energy at infinity to be zero).
Mass of the earth = 6.0Ã— 1024 kg, radius = 6400 km.

**Question 8.23** 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 = 2Ã— 1030 kg).

**Question 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 = 1000 kg;
mass of the sun = 2Ã— 1030 kg; mass of mars = 6.4Ã— 1023 kg; radius of mars = 3395 km;
radius of the orbit of mars = 2.28 Ã— 108 km; G = 6.67Ã— 10-11 N m2 kgâ€“2.

**Question 8.25** A rocket is fired â€˜verticallyâ€™ from the surface of mars with a speed of 2 km sâ€“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 = 6.4Ã— 1023
kg; radius of mars = 3395 km; G = 6.67Ã— 10-11 N m2 kgâ€“2.

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- Chapter 1 Physical World
- Chapter 2 Units And Measurement
- Chapter 3 Motion In A Straight Line
- Chapter 4 Motion In A Plane
- Chapter 5 Laws Of Motion
- Chapter 7 Systems of Particles and Rotational Motion
- Chapter 6 Work Energy and Power
- Chapter 8 Gravitation
- Chapter 9 Mechanical Properties Of Solids
- Chapter 10 Mechanical Properties Of Fluids
- Chapter 11 Thermal Properties of Matter
- Chapter 12 Thermodynamics
- Chapter 13 Kinetic Theory
- Chapter 14 Oscillations
- Chapter 15 Waves

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