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(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 spaceship 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. However, the tidal effect of the moon's pull is greater than the tidal effect of Sun. Why ?
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(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
is
more/less accurate than the formula mg
for the
difference
of potential energy between two points
and
distance
away from the centre of earth.
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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 ?
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One of the satellites of Jupiter, has an orbital period of
1-769 days and the radius of the orbit is
Show that
mass of Jupiter is about one thousand times that of the sun. (lake 1 year =
365.25 mean solar day).
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Let us consider that our galaxy consists of
stars each
of one solar mass. How long will this star at a distance of 50,000 ly from the
galactic centre take to complete one revolution ? lake the diameter of the
Milky way to be
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Choose the correct alternative :
(a) If the zero of the potential energy is at infinity, the total energy of an orbiting satellite is negative of its kinetic/potential energy.
(b) The energy required to rocket 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.
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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 ? Explain your answer.
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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.
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Which of the following symptoms is likely to affect an astronaut in space (a) swollen feet (b) swollen face, (c) headache, (d) orientational problem.
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The gravitational intensity at the centre Q
of
the
drumhead defined by a hemispherical shell of uniform mass density has the
direction indicated by the arrow (6(NCT).l), (i) a, (ii) b , (iii)
c, (iv) zero.
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For the above problem, the direction of the gravitational intensity at any arbitrary point P is indicated by the arrow (i) d, (ii) e, (iii)/, (iv) g.
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A rocket is fired from the earth towards the sun. At what
point on its path is the gravitational force on the rocket zero ? Mass of sun =
Mass of
earth =
Neglect
the effect of other planets. Orbital radius of earth =
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How will you 'weigh the Sun', that is estimate its mass ?
You will need to now the period of one of its planets and the radius of the
planetary orbit. The mean orbital radius of the Earth around the Sun is
.
Estimate the mass of the Sun.
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A Saturn year is 29-5 times the earth year. How far is the
Saturn from the sun if the earth is
km away
from the sun ?
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A body weighs 63 N on the surface of Earth . What is the gravitational force on it due to the Earth at a height equal to half the radius of the Earth ?
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Assuming the earth to be a sphere of uniform mean density,
how much would a body weigh half way down to the centre of earth if it weighed
250 N on the surface ? g on the surface of earth is
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A rocket is fired vertically with a speed of 5 km
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 earth =
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The escape velocity of projectile on the surface of earth
is 11-2 km
. If a
body is projected out with thrice of this speed, find the speed of the body far
away from the earth. Ignore the presence of other planets and sun.
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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 gravitational influence of earth ? Mass of the satellite is 200 kg, mass of
the earth =
radius of
the earth
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Two stars each of 1 solar mass
are
approaching each other for a head on collision. When they are at a distance
km,
their speeds are negligible. What is the speed with which they collide ? The
radius of each star is
km.
Assume the stars to remain undisturbed until they collide. Use the known value
of G.
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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 field 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.
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A geostationary satellite orbits the earth at a height of
nearly 36,000 km from the surface of 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 =
6400 km,
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A star 2-5 times the mass of the sun and
collapsed to a size of the 12 km rotates with a speed of 1
5 rev.
per second. (Extremely compact stars of this kind are known as neutron stars.
Certain observed steller objects called pulsars are believed to belong this
category). Will an object placed on its equator
remain
struck to its surface due to gravity ? (Mass of the sun
).
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A space-ship is stationed on Mars. How much must be
expended on the spaceship to rocket it out of the solar system ? Mass of the
spaceship = 1000 kg, Mass of the Sun
Mass of the
Mars
Radius
of Mars = 3395 km. Radius of the orbit of Mars
G
= 6-67 x 10-11 N m 2 kg-2.
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A rocket is fired vertically from the surface of Mars with a
speed of 2 km
If
20% of its initial kinetic 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 = 3395 km ;
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question_answer26)
The earth is an
approximate sphere. If the interior contained matter which is not of the same
density everywhere, then on the surface of the earth, the acceleration due to
gravity
(a)
will be directed towards the centre but not the same everywhere.
(b)
will have the same value everywhere but not directed towards the centre.
(c)
will be same everywhere in magnitude directed towards the centre.
(d)
cannot be zero at any point.
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question_answer27)
As
observed from earth, the sun appears to move in an approximate circular orbit.
For the motion of another planet like mercury as observed from earth, this
would
(a)
be similarly true.
(b)
not be true because the force between earth and mercury is not inverse square
law.
(c)
not be true because the major gravitational force on mercury is due to sun.
(d)
not be true because mercury is influenced by forces other than gravitational
forces.
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question_answer28)
Different
points in earth are at slightly different distances from the sun and hence
experience different forces due to gravitation. For a rigid body, we know that
if various forces act at various points in it, the resultant motion is as if a
net force acts on the c.m. (centre of mass) causing translation and a net
torque at the c.m. causing rotation around an axis through the c.m. For the
earth-sun system (approximating die earth as a uniform density sphere)
(a)
die torque is zero.
(b)
the torque causes the earth to spin.
(c)
the rigid body result is not applicable since the earth is not even approximately
a rigid body.
(d)
the torque causes die earth to move around die sun.
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question_answer29)
Satellites
orbiting the earth have finite life and sometimes debris of satellites fall to
the earth. This is because,
(a)
the solar cells and batteries in satellites run out.
(b)
the laws of gravitation predict a trajectory spiralling inwards.
(c)
of viscous forces causing the speed of satellite and hence height to gradually
decrease.
(d)
of collisions with other satellites.
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question_answer30)
Both
earth and moon are subject to the gravitational force of the sun. As observed
from the sun, die orbit of die moon
(a)
will be elliptical.
(b)
will not be strictly elliptical because the total gravitational force on it is
not central.
(c)
is not elliptical but will necessarily be a closed curve.
(d)
deviates considerably from being elliptical due to influence of planets other
than earth.
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question_answer31)
In
our solar system, die inter-planetary region has chunks of matter (much smaller
in size compared to planets) called asteroids. They
(a)
will not move around the sun since they have very small masses compared to sun.
(b)
will move in an irregular way because of their small masses and will drift away
into outer space.
(c)
will move around the sun in closed orbits but not obey Kepler's laws.
(d)
will move in orbits like planets and obey Kepler?s laws.
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question_answer32)
Choose
the wrong option:
(a)
Inertial mass is a measure of difficulty of accelerating a body an external
force whereas the gravitational mass is relevant in determining the
gravitational force on it by an external mass.
(b)
The gravitational mass and inertial mass are equal is an experimental result.
(c)
That the acceleration due to gravity on earth is the same for all bodies is due
to the equality of gravitational mass and inertial mass.
(d)
Gravitational mass of a particle like proton can depend on the presence of
neighouring heavy objects but the inertial mass cannot.
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question_answer33)
Particles
of masses 2M, m and M are respectively at points A, B and C with \[AB=1/2\,(BC)\].
m is much-much smaller than M and at time t = 0, they are all at rest
At
subsequent times before any collision takes place :
(a) m will remain
at rest.
(b) m will move
towards M.
(c) m will move
towards 2M.
(d) m will have
oscillatory motion.
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question_answer34)
Which of the
following options are correct?
(a)
Acceleration due to gravity decreases with increasing altitude.
(b)
Acceleration due to gravity increases with increasing depth (assume the earth
to be a sphere of uniform density).
(c)
Acceleration due to gravity increases with increasing latitude.
(d)
Acceleration due to gravity is independent of the mass of the earth.
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question_answer35)
If the law of
gravitation, instead of being inverse-square law, becomes an inverse-cube law-
(a)
planers will not have elliptic orbits.
(b)
circular orbits of planets is not possible
(c)
projectile motion of a stone thrown by hand on the surface of the earth will be
approximately parabolic.
(d)
there will be no gravitational force inside a spherical shell of uniform
density.
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question_answer36)
If
the mass of sun where ten times smaller and gravitational constant G were ten
times larger in magnitudes.
(a)
walking on ground would became more difficult.
(b)the
acceleration due to gravity on earth will not change.
(c)
raindrops will fall much faster.
(d)
airplanes will have to travel much faster.
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question_answer37)
If
the sun and the planets carried huge amounts of opposite charges.
(a)
all three of Kepler?s laws would still be valid.
(b)
only the third law will be valid.
(c)
the second law will not change.
(d)
the first law will still be valid.
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question_answer38)
There have been
suggestions that the value of the gravitational constant G becomes smaller when
considered over very large time period (in billions of years) in the further.
If that happens, for our earth,
(a) nothing will
change.
(b)
we will become hotter after billions of years.
(c)
we will be going around but not strictly in closed orbits.
(d)
after sufficiently long time we will leave the solar system.
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question_answer39)
Supposing
Newton?s law of gravitation for gravitation force \[{{F}_{1}}\] and \[{{F}_{2}}\]
between two
masses \[{{m}_{1}}\] and
\[{{m}_{2}}\] at
positions \[{{r}_{1}}\] and
\[{{r}_{2}}\] read
\[{{F}_{1}}=-{{F}_{2}}=\frac{{{{\vec{r}}}_{12}}}{r_{12}^{3}}\,\,GM_{0}^{2}\,\,{{\left(
\frac{{{m}_{1}}{{m}_{2}}}{M_{0}^{2}} \right)}^{n}}\] where \[{{M}_{o}}\]
is a constant of dimension of mass, \[{{r}_{12}}={{r}_{1}}-{{r}_{2}}\] and N is a number.
In such a case.
(a)
the acceleration due to gravity on earth will be different for different
objects.
(b)
none of the three laws of Kepler will be valid.
(c)
only the third law will become invalid.
(d)
for n negative, an object lighter than water will sink in water.
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question_answer40)
Which
of die following are true?
(a)
A polar satellite goes around the earth's pole in north-south direction.
(b)
A geostationary satellite goes around die earth in east-west direction.
(c)
A geostationary satellite goes around die earth in west-east direction.
(d)
A polar satellite goes around the earth in east-west direction.
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question_answer41)
The
centre of mass of an extended body on die surface of the earth and its centre
of gravity
(a)
are always at the same point for any size of die body.
(b)
are always at die same point only for spherical bodies.
(c)
can never be at the same point.
(d)
is close to each other for objects, say of size less than 100 m.
(e)
both can change if the object is taken deep inside the earth.
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question_answer42)
Molecules
in air in the atmosphere are attracted by gravitational force of the each.
Explain why all of them do not fall into the earth just like an apple falling
from a tree.
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question_answer43)
Give
one example each of central force and non-central force.
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question_answer44)
Draw
areal velocity versus time graph for mars.
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question_answer45)
What
is the direction of areal velocity of the earth around the sun?
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question_answer46)
How
is the gravitational force between two point masses affected when they are
dipped in water keeping die separation between them the same?
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question_answer47)
Is
it possible for a body to have inertia but not weight?
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question_answer48)
We
can shield a charge from electric fields by putting it inside a hollow
conductor. Can we shield a body from the gravitational influence of nearby
matter by putting it inside a hollow sphere or by some other mean?
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question_answer49)
An
astronaut inside a small spaceship orbiting around the earth cannot detect
gravity. If die space station orbiting around the earth has a large size, can
he hope to detect gravity?
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question_answer50)
The
gravitational force between a hollow spherical shell (of radius R and uniform
density) and a point mass is F. Show the nature of F vs r graph where r is the
distance of the point from the centre of the hollow spherical shell of uniform
density.
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question_answer51)
Out
of aphelion and perihelion, where is the speed of the earth more and why?
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question_answer52)
What
is the angle between the equatorial plane and the orbital plane of
(a)
Polar satellite?
(b)
Geostationary satellite
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question_answer53)
Mean
solar day is the time interval between two successive noon when sun passes
through zenith point (meridian).
Sidereal
day is the time interval between two successive transit of a distance star
through the zenith point (meridian).
By
drawing appropriate diagram showing earth?s spin and orbital motion, show that
mean solar day is four minutes longer than the sidereal day. In other words,
distant stars would rise 4 minutes early every successive day.
(Hint:
you may assume circular orbit for the earth).
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question_answer54)
Two
identical heavy spheres are separated by a distance 10 times their radius. Will
an object placed at the mid point of the line joining their centres be in
stable equilibrium or unstable equilibrium? Give reason for your answer.
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question_answer55)
Show
the nature of the following graph for a satellite orbiting die earth.
(a)
KE \[\upsilon s\] orbital
radius R
(b)
PE \[\upsilon s\] orbital
radius R
(c)
TE \[\upsilon s\] orbital
radius R.
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question_answer56)
Shown
are several curves (Fig.). Explain with reason, which ones amongst them can be
possible trajectories traced by a projectile (neglect air friction).
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question_answer57)
An
object of mass m is raised from the surface of the earth to a height equal to
the radius of the earth, that is, taken from a distance R to 2R from the centre
of the earth. What is the gain in its potential energy?
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question_answer58)
A
mass m is placed at P a distance h along the normal through the centre O
of a thin circular ring of mass M and radius r (Fig.).
If
the mass is removed further away such that OP becomes 2h, by what factor
the force of gravitation will decrease, if \[h=r\]?
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question_answer59)
A
star lie the sun has several bodies moving around it as different distances.
Consider that all of them are moving in circular orbits. Let r be the distance
of the body from the centre of the star and let its linear velocity be \[\upsilon
\], angular velocity \[\omega \], kinetic energy K, gravitational potential
energy U, total energy E and angular momentum \[l\]. As the radius \[r\] of the
orbit increases, determine which of the above quantities increase and which
ones decrease.
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question_answer60)
Six
point masses of mass \[m\] each are at the vertices of a regular hexagon of side
1. Calculate the force on any of the masses.
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question_answer61)
A
satellite is to be placed in equatorial geostationary orbit around earth for
communication.
(a)
Calculate height of such a satellite.
(b)
Find out the minimum number of satellites that are needed to cover entire earth
so that at least one satellites is visible from any point on the equator.
[\[M=6\times
{{10}^{24}}\,\,kg,\,R=6400\,km,\,\]\[25th,\,\,G=6.67\]\[\times
{{10}^{-11}}\,SI\]units]
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question_answer62)
Earth's
orbit is an ellipse with eccentricity 0.0167. Thus, earth's distance from the
sun and speed as it moves around the sun varies from day to day. This means
that the length of the solar day is not constant through the year. Assume that
earth's spin axis is normal to its orbital plane and find out the length of the
shortest and the longest day. A day should be taken from noon to noon. Does
this explain variation of length of the day during the year?
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question_answer63)
A
satellite is in an elliptic orbit around the earth with aphelion of 6R and
perihelion of 2 R where \[R=6400\,\,km\] is the radius of the earth. Find
eccentricity of the orbit. Find the velocity of the satellite at apogee and perigee.
What should be done if this satellite has to be transferred to a circular orbit
of radius 6R?
[\[G=6.67\times
{{10}^{-11}}\,SI\] units
and \[M=6\times {{10}^{24}}\,kg\]]
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