Additional Questions - Chapter 6 Gravitation 11th Science Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

Additional Questions
I. Choose the correct answer from the following:
Question 1.
According to Kepler, planet move in
(a) Circular orbits around the Sun
(b) Elliptical orbits around the Sim with Sun at exact centre
(c) Straight lines with constant velocity '
(d) Elliptical orbits around the Sun with Sun at one of its foci.
Answer:
(d) Elliptical orbits around the Sun with Sun at one of its foci.
Question 2.
Kepler's second law regarding constancy of aerial velocity of a planet is consequence of the law of conservation of
(a) energy
(b) angular momentum
(c) linear momentum
(d) None of these
Answer:

(b) angular momentum
Hint:
$$
\frac{d \mathrm{~A}}{d t}=\frac{\mathrm{L}}{2 m}=\text { constant }
$
Question 3.
According to Kepler, the period of revolution of a planet (T) and its mean distance from the Sun (a) are related by the equation
(a) $\mathrm{T}^3 \mathrm{a}^3=$ constant
(b) $\mathrm{T}^2 \mathrm{a}^{-3}=$ constant
(c) $\mathrm{Ta}^3=$ constant
(d) $\mathrm{T}^2 \mathrm{a}=$ constant
Answer:
(b) $\mathrm{T}^2 \mathrm{a}^{-3}=$ constant
Hint:
$
\frac{T^2}{a^3}=\text { constant, } T^2 a^{-3}=\text { constant }
$
Question 4.
The period of Moon's rotation around the Earth is nearly 29 days. If Moon's mass were 2 fold
its present value and all other things remained unchanged the period of Moon's rotation would be nearly ..... days.

(a) $29 \sqrt{2}$
(b) $\frac{29}{\sqrt{2}}$
(c) $29 \times 2$
(d) 29
Answer:
(d) 29
Hint:
Time period does not depends upon the mass of satellite.
Question 5.
The period of revolution of planet A around the Sun is 8 times that of B. The distance of A from the Sun is how many times greater than that of B from the Sun.
(a) 2
(b) 3
(c) 4
(d) 5
Answer:

(c) 4
Hint:
$
\begin{aligned}
\left(\frac{\mathrm{T}_{\mathrm{A}}}{\mathrm{T}_{\mathrm{B}}}\right)^2 & =\left(\frac{a_{\mathrm{A}}}{a_{\mathrm{B}}}\right)^2 \Rightarrow\left(\frac{8 \mathrm{~T}_{\mathrm{B}}}{\mathrm{T}_{\mathrm{B}}}\right)^{\frac{2}{3}}=\frac{a_{\mathrm{A}}}{a_{\mathrm{B}}} \\
\mathrm{T}_{\mathrm{A}} & =8 \mathrm{~T}_{\mathrm{B}} \Rightarrow(8)^{\frac{2}{3}} a_{\mathrm{B}}=a_{\mathrm{A}} \Rightarrow a_{\mathrm{A}}=4 a_{\mathrm{B}}
\end{aligned}
$
Question 6.
The radius of orbit of a planet is two times that of Earth. The time period of planet is years....
(a) 4.2
(b) 2.8
(c) 5.6
(d) 8.4
Answer:
(b) 2.8
Hint:
$
\mathrm{T}_2=\mathrm{T}_1\left(\frac{a_2}{a_1}\right)^{\frac{3}{2}} \Rightarrow \mathrm{T}_2=1 \times(2)^{\frac{3}{2}}=2.8 \text { years }
$

Question 7.
A geostationary satellite orbits around the earth in a circular orbit of radius $3600 \mathrm{~km}$ the time period of a satellite orbiting a few hundred kilometers above the earth's surface $\left(\mathrm{R}_{\mathrm{E}}=6400 \mathrm{~km}\right)$ will be approximately be hours.
(a) $1 / 2$
(b) 1
(c) 2
(d) 4
Answer:
(c) 2
Hint:
$
\frac{\mathrm{T}_2}{\mathrm{~T}_1}=\left(\frac{a_2}{a_1}\right)^{\frac{3}{2}} \Rightarrow \mathrm{T}_2=24\left(\frac{6400}{3600}\right)^{\frac{3}{2}}=2 \text { hours }
$
Question 8.
What does not change in the field of central force?

(a) Potential energy
(b) kinetic energy
(c) linear momentum
(d) Angular momentum
Answer:
(d) Angular momentum
Hint:
For central force torque is zero.
$
\therefore \tau=\frac{d L}{d t}=0 \Rightarrow \mathrm{L}=\text { constant }
$
Question 9.
A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the center of earth in new orbit is two times of the earlier orbit. The time period in second orbit is hours.
(a) 4.8
(b) $48 \sqrt{2}$
(c) 24
(d) 24
Answer:
(b) $48 \sqrt{2}$
Hint:
Hint: $\mathrm{T} \propto r^{\frac{3}{2}}$ if $r$ becomes double then time period will become $(2)^{\frac{3}{2}}$ tim period will be $24 \times 2 \sqrt{2}$ hours. i.e., $48 \sqrt{2}$ hours.

Question 10.
If the Earth is at one-fourth of its present distance from the sun the duration of year will be:
(a) half the present year
(b) one-eight the present year
(c) one-fourth the present year
(d) one-sixth the present year
Answer:
(b) one-eight the present year
Hint:
$
\mathrm{T}^2 \propto a^3 ; \therefore\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}\right)^2=\left(\frac{1}{4}\right)^3 \Rightarrow \mathrm{T}_1=\frac{1}{8} \mathrm{~T}_2
$
Question 11.
The Earth E moves in an elliptical orbit with the Sun $\mathrm{S}$ at one of the foci as shown in figure.
Its speed of motion will be maximum at a point ........

(a) $\mathrm{C}$
(b) $\mathrm{A}$
(c) $\mathrm{B}$
(d) D
Answer:
(b) $\mathrm{A}$
Hint: Speed at the Earth will be maximum when its distance from the Sun is minimum because $\mathrm{mvr}=\mathrm{constant}$
Question 12.
Rockets are launched in eastward direction to take advantage of .....
(a) the clear sky on eastern side
(b) Earth's rotation
(c) the thinner atmosphere on this side
(d) Earth's tilt
Answer:
(b) Earth's rotation
Hint:
Because Earth rotation from west to east direction.
Question 13.
Two sphere of mass $M_1$ and $M_2$ are situated in air and the gravitational force between them is F. The space around the masses is now filled with liquid of specific gravity 3 . The gravitational force will now be .....
(a) $\mathrm{F}$
(b) $3 \mathrm{~F}$
(c) $\frac{\mathrm{F}}{3}$
(d) $\frac{\mathrm{F}}{9}$

Answer:
(a) $\mathrm{F}$
Hint:
Gravitational force does not depend upon the medium.
Question 14.
Which of the following statement about the gravitational constant is true?
(a) It is a force
(b) It has same value in all system of unit
(c) It has not unit
(d) It depends on the value of the masses
Answer:
(a) It is a force
Question 15.
Energy required to move a body of mass ' $M$ ' from an orbit of radius $2 R$ to $3 R$ is
(a) $\frac{\mathrm{GM}}{12 \mathrm{R}}$
(b) $\frac{\mathrm{GM} m}{3 \mathrm{R}^2}$
(c) $\frac{\mathrm{GMm}}{8 \mathrm{R}}$
(d) $\frac{\mathrm{GMm}}{6 \mathrm{R}}$

Answer:

(d) $\frac{\mathrm{GMm}}{6 \mathrm{R}}$
Hint:
Change in P.E. in displacing a body from $r_1$ and $r_2$ is given by:
$
\Delta \mathrm{U}=\mathrm{GMm}\left[\frac{1}{r_1}-\frac{1}{r_2}\right]=\mathrm{GM} m\left[\frac{1}{2 \mathrm{R}}-\frac{1}{3 \mathrm{R}}\right]=\frac{\mathrm{GM} m}{6 \mathrm{R}}
$
Question 16.
The mass of the earth is $6 \times 10^{24} \mathrm{~kg}$ and that of the Moon is $7.4 \times 10^{22} \mathrm{~kg}$. The constant of gravitation $\mathrm{G}$ is $6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$. The potential energy of the system is -7.79 $\times 10^{28} \mathrm{~J}$. The mean distance between the Earth and Moon is ..... metre.
(a) $3.80 \times 10^8$
(b) $3.37 \times 10^8$
(c) $7.60 \times 10^8$
(d) $1.90 \times 10^2$
Answer:
(a) $3.80 \times 10^8$
Hint:
$
\mathrm{U}=\frac{-\mathrm{GMm}}{r} \Rightarrow r=3.8 \times 10^8 \mathrm{~m}
$
Question 17.
What is the intensity of gravitational field at the center of spherical shell?

(a) $\frac{\mathrm{G} m}{r^2}$
(b) $g$
(c) zero
(d) None of these
Answer:
(c) zero
Question 18.
A body of mass $\mathrm{m}$ is taken from the Earth's surface to a height equal to the radius $\mathrm{R}$ of the earth. If $g$ is the acceleration to gravity at the surface of the Earth, then find the change in the potential energy of the body ......
(a) $\frac{1}{4} m g \mathrm{R}$
(b) $\frac{1}{2} m g R$
(c) $m g \mathrm{R}$
Answer:
(b) $\frac{1}{2} m g R$
Hint:
Change in P.E. $=\frac{-\mathrm{GMm}}{\mathrm{R}+\mathrm{R}}-\left(-\frac{\mathrm{GM} m}{\mathrm{R}}\right)=\frac{\mathrm{GM} m}{2 \mathrm{R}}=\frac{1}{2} m g \mathrm{R}$
Question 19.
A satellite is orbiting around the Earth in a circular orbit with velocity $\mathrm{v}$. If $m$ is the mass of the satellite, its total energy is ......
(a) $m v^2$
(b) $\frac{1}{2} m v^2$
(c) $-\frac{1}{2} m v^2$

Answer:
(c) $-\frac{1}{2} m v^2$
Hint:
The total energy is negative of the kinetic energy.
Question 20.
Escape velocity of a body of $1 \mathrm{~kg}$. On a planet is $100 \mathrm{~ms}^{-1}$. Gravitational potential energy of the body at the planet is
(a) $-5000 \mathrm{~J}$
(b) $-1000 \mathrm{~J}$
(c) $-2400 \mathrm{~J}$
(d) $4000 \mathrm{~J}$
Answer:
(a) $-5000 \mathrm{~J}$

$
\begin{aligned}
& \text { Hint: } v_e=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \Rightarrow(100)^2=\frac{2 \mathrm{GM}}{\mathrm{R}} \Rightarrow \frac{\mathrm{GM}}{\mathrm{R}}=5000 \\
& \therefore \text { P.E., } \mathrm{U}=-\frac{\mathrm{GM} m}{\mathrm{R}}=-5000 \mathrm{~J}
\end{aligned}
$
Question 21.
A particle falls towards earth from infinity. It's velocity reaching the Earth would be
(a) infinity
(b) $\sqrt{2 g R}$
(c) $2 \sqrt{g \mathrm{R}}$
(d) zero
Answer:
(b) $\sqrt{2 g \mathrm{R}}$
Hint:
This should be equal to escape velocity is $=\sqrt{2 g \mathrm{R}}$
Question 22.
An artificial satellite is revolving round the Earth in a circular orbit, its velocity is half the escape velocity. Its height from the Earth surface is .... $\mathrm{km}$.
(a) 6400
(b) 12800
(c) 3200
(d) 1600
Answer:
(a) 6400

Question 23.
The escape velocity of a body on the surface of the Earth is $11.2 \mathrm{~km} / \mathrm{s}$. If the mass of the Earth is increase to twice its present value and the radius of the earth becomes half, the escape velocity becomes $=\ldots \ldots \mathrm{kms}^{-1}$
(a) 5.6
(b) 11.2
(c) 22.4
(d) 494.8
Answer:
(c) 22.4
Hint:
$
v_e=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}
$

If $\mathrm{M}$ becomes double and $\mathrm{R}$ becomes half, then escape velocity becomes two times.
Question 24.
The velocity with which a projectile must be fired so that it escapes Earth's gravitational does not depend on .......
(a) Mass of Earth
(b) Radius of the projectile's orbit
(c) Mass of the projectile
(d) Gravitational constant
Answer:
(c) Mass of the projectile
Question 25.
The escape velocity for a body projected vertically upwards from the surface of Earth is $11 \mathrm{kms}^{-1}$. If the body is projected at an angle of $45^{\circ}$ with the vertical, the escape velocity will be $\ldots . \mathrm{kms}^{-1}$
(a) $\frac{11}{\sqrt{2}}$
(b) $11 \sqrt{2}$
(c) 22
(d) 11
Answer:
(d) 11
Hint:
Escape velocity does not depends upon the angle of projection.

Question 26.
Two satellites of mass $\mathrm{ml}$ and $\mathrm{m}_2\left(\mathrm{~m}_1>\mathrm{m}_2\right)$ are revolving round the earth in circular orbits of $r_1$ and $r_2\left(r_1>r_2\right)$ respectively. Which of the following statement is true regarding their speeds $\mathrm{v}_1$ and $\mathrm{v}_2$
(a) $v_1=v_2$
(b) $v_1 (c) $v_1>v_2$
(d) $\frac{v_1}{r_1}$
Answer:
(b) $\mathrm{v}_1<\mathrm{v}_2$
Hint:
$v=\sqrt{\frac{\mathrm{GM}}{r}}$ it $r_1>r_2$ then $v_1

Question 27.
As astronaut orbiting the earth in a circular orbit $120 \mathrm{~km}$ above the surface of Earth, gently drops a spoon out of space-ship. The spoon will
(a) fall vertically down to the Earth
(b) move towards the moon
(c) will move along with space-ship
(d) will move in an irregular way then fall down to Earth
Answer:
(c) will move along with space-ship
Hint:
The velocity of the spoon will be equal to the orbital velocity when dropped out of the space-ship
Question 28.
A satellite revolves around the Earth in an elliptical orbit. Its speed.
(a) is the same at all point in the orbit
(b) is greatest when it is closest to the Earth
(c) is greatest when it is farthest to the Earth
(d) goes on increasing or decreasing continuously depending upon the mass of the satellite. Answer:
(b) is greatest when it is closest to the Earth
Question 29.
A satellite is moving around the Earth with speed $\mathrm{v}$ in a circular orbit of radius $r$. If the orbit
radius is decreased by $1 \%$ its speed will
(a) increase by $1 \%$
(b) increase by $0.5 \%$

(c) decrease by $1 \%$
(d) decrease by $0.5 \%$
Answer:
(b) increase by $0.5 \%$
$v \propto \frac{1}{\sqrt{r}}, \%$ increase in speed $=\frac{1}{2} \%$ decrease in radius $=\frac{1}{2}(1 \%)=0.5 \%$

Question 30.
Orbital velocity of an artificial satellite does not depend upon .......
(a) mass of Earth
(b) mass of satellite
(c) radius of Earth
(d) acceleration due to gravity
Answer:
(b) mass of satellite
Question 31.
The orbital speed of Jupiter is .......
(a) greater than the orbital speed of Earth
(b) less then the orbital speed of Earth
(c) zero
(d) equal to the orbital speed of Earth
Answer:
(b) less then the orbital speed of Earth
Hint:
$
\frac{v_j}{v_e}=\frac{r_e}{r_j}, \text { as } r_j>r_e \text { therefore } v_j $
Question 32.
As we go grom the equator to the poles, the value of $g . \ldots$.
(a) remains constant
(b) decreases
(c) increases
(d) decreases upto latitude of $45^{\circ}$

Answer:
(c) increases
Question 33.
The value of $g$ on the Earth surface is $980 \mathrm{~cm} / \mathrm{sec}^2$. Its value at a height of $64 \mathrm{~km}$ from the Earth surface is $\ldots \ldots . \mathrm{cms}^2$
(a) 960.40
(b) 984.90
(c) 982.45
(d) 977.55
Answer:
(a) 960.40

Hint:
$
\frac{g^{\prime}}{g}=\left(\frac{\mathrm{R}}{\mathrm{R}+h}\right)^2 \Rightarrow g^{\prime}=g\left(\frac{6400}{6400+64}\right)^2=960.40 \mathrm{cms}^{-2}
$
Question 34.
The Moon s radius is $\frac{1}{4}$ that of earth and its mass is $\frac{1}{80}$ times that of the Earth. If $g$ represents the acceleration due to gravity on the surface of Earth, that on the surface of the Moon is .....
(a) $\frac{g}{4}$
(b) $\frac{g}{5}$
(c) $\frac{g}{6}$
(d) $\frac{g}{8}$
Answer:
(b) $\frac{g}{5}$
Hint:
Using: $g=\frac{\mathrm{GM}}{\mathrm{R}^2}$ we get $g_m=\frac{g}{5}$
Question 35.
If the density of small planet is that of the same as that of the earth while the radius of the
planet is 0.2 times that of the Earth, the gravitational acceleration on the surface for the planet is....
(a) $0.2 \mathrm{~g}$
(b) $0.4 \mathrm{~g}$

(c) $2 \mathrm{~g}$
(d) $4 \mathrm{~g}$
Answer:
(a) $0.2 \mathrm{~g}$
Hint:
$g=\frac{4}{3} \pi \mathrm{GR} \rho$ and $g^{\prime}=\frac{4}{3} \pi \mathrm{GR}^{\prime} \rho ; \frac{g^{\prime}}{g}=\frac{\mathrm{R}^{\prime}}{\mathrm{R}}=0.2 \Rightarrow g^{\prime}=0.2 g$
Question 36.
Assuming Earth to be a sphere of a uniform density, what is value of gravitational acceleration in mine $100 \mathrm{~km}$ below the Earth surface $=\ldots . \mathrm{ms}^{-2}$
(a) 9.66
(b) 7.64
(c) 5.00
(d) 3.1
Answer:
(a) 9.66

Hint:
$
g^{\prime}=g\left[1-\frac{d}{\mathrm{R}}\right]=9.66 \mathrm{~ms}^{-2}
$
Question 37.
The radii of two planets are respectively $\mathrm{R}_1$ and $\mathrm{R}_2$ and their densities are respectively $\rho_1$ and $\rho_2$ the ratio of the accelerations due to gravity at their surface is ......
(a) $g_1: g_2=\frac{\rho_1}{R_1^2}: \frac{\rho_2}{R_2^2}$
(b) $g_1: g_2=\mathrm{R}_1 \mathrm{R}_2: \rho_1 \rho_2$
(c) $g_1: g_2=\mathrm{R}_1 \rho_2: \mathrm{R}_2 \rho_1$
(d) $g_1: g_2=\mathrm{R}_1 \rho_1: \mathrm{R}_2 \rho_2$
Answer:
(d) $g_1: g_2=\mathrm{R}_1 \rho_1: \mathrm{R}_2 \rho_2$
Using $g=\frac{4}{3} \pi \mathrm{GR} \rho ; \frac{g_1}{g_2}=\frac{\mathrm{R}_1 \rho_1}{\mathrm{R}_2 \rho_2}$
Question 38.
The acceleration due to gravity near the surface of a planet of radius $\mathrm{R}$ and density $\mathrm{d}$ is proportional to:
(a) $\frac{d}{\mathrm{R}^2}$
(b) $d \mathrm{R}^2$
(c) $d \mathrm{R}$
(d) $\frac{d}{\mathrm{R}}$
Answer:
(c) $d R$

Hint:
$
g=\frac{4}{3} \pi \rho \mathrm{GR} \Rightarrow g \propto d \mathrm{R}(\rho=d)
$
Question 39.
The acceleration of a body due to the attraction of the Earth (radius $\mathrm{R}$ ) at a distance $2 \mathrm{R}$ from the surface of the Earth is .......
(a) $\frac{g}{9}$
(b) $\frac{g}{3}$
(c) $\frac{g}{4}$
(d) 9
Answer:
(a) $\frac{g}{9}$
Hint:
$
g^{\prime}=g\left(\frac{\mathrm{R}}{\mathrm{R}+2 \mathrm{R}}\right)^2=\frac{g}{9}
$

Question 40.
If density of Earth increased 4 times and its radius becomes half of then out weight will be ......
(a) four times its present value
(b) doubled
(c) remains same
(d) halved
Answer:
(b) doubled
Hint:
$g \propto \rho R$
Question 41.
The radius of the Earth is $6400 \mathrm{~km}$ and $g=10 \mathrm{~ms}^{-2}$ in order that a body of $5 \mathrm{~kg}$ weights zero at the equator, the angular speed of the Earth is ..... $\mathrm{rad} \mathrm{s}^{-1}$
(a) $\frac{1}{80}$
(b) $\frac{1}{400}$
(c) $\frac{1}{800}$
(d) $\frac{1}{60}$
Answer:
(c) $\frac{1}{800}$
Hint:
For condition of weightlessness at equator $\omega=\sqrt{\frac{g}{R}}=\frac{1}{800} \mathrm{rad} / \mathrm{sec}$

Question 42.
Weight of a body is maximum at .....
(a) Moon
(b) poles of Earth
(c) equator of Earth
(d) centre of Earth
Answer:
(b) poles of Earth
Question 43.
The weight of an astronaut, in an artificial satellite revolving around the Earth is:
(a) zero
(b) equal to that on the Earth
(c) more than that on Earth
(d) less than that on Earth
Answer:
(a) zero

2 Marks Questions
Question 1.
Distinguish between the terms gravitation and gravity.
Answer:
Gravitation: It is the force of attraction between any two bodies in the universe. Gravity: It is the force of attraction between the earth and any object lying on or near its surface.
Question 2.
Why is $\mathrm{G}$ called the universal gravitational constant?
Answer:
The value of $G$ does not depend on the nature and size of the bodies. It also does not depend on the nature of the medium between the two bodies. That is why $\mathrm{G}$ is called universal gravitational constant.
Question 3.
What is meant by the term free fall?
Answer:
The motion of a body under the influence of gravity alone is called a free fall.
Question 4.
What is meant by acceleration due to gravity? Is is a scalar or a vector?
Answer:
The acceleration produced in a freely falling body under the gravitational pull of the earth. It is a vector having direction towards the centre of the earth.

Question 5.
What do you mean by weight of a body? Is it a scalar or vector?
Answer:
Weight of a body is defined as the gravitational force with which a body is attracted towards the centre of the earth. Hence the weight of a body is given by $w=m g$ (or) $\overrightarrow{\mathrm{W}}=m \vec{g}$
Question 6.
Define orbital velocity.
Answer:
Orbital velocity is the velocity required to put the satellite into its orbit around the earth.
Question 7.
Give some uses of geostationary satellites.
Answer:
- In communicating radio, T.V and telephone signals across the world.
- In studying upper regions of the atmosphere.

- In forecasting weather.
- In deter ming the exact shape and dimensions of the earth.
- In studying solar radiations and cosmic rays.
Question 8.
Give the uses of polar satellites.
Answer:
- Polar satellites are uses in weather and environment monitoring.
- They are used in spying work for military purposes.
- They are used to study topography of Moon, Venus and Mars.