Download Gravitation

AL-MC-Gravitation / p.1
1.
2.
(88-I-8)
A.
–4 kJ.
A satellite moving round the Earth in a circular
B.
–2 kJ.
orbit of radius R has a period T. What would the
C.
+2 kJ.
period be if the orbit were of radius R/4?
D.
+4 kJ.
E.
+8 kJ.
A.
T/8
B.
T/4
C.
T/2
In which of the following situations is the
D.
2T
magnitude of the normal reaction of the supporting
E.
4T
surface, R, equal to the weight of the body, mg?
4.
(91-I-1)
(89-I-11)
(1)
At rest on a rough inclined plane.
Assuming the Earth to be a perfect sphere, what
(2)
On the floor of a spacecraft in circular orbit
would its angular velocity of rotation have to be
around the earth.
for an object at the equator to be weightless (i.e. to
(3)
give a spring balance reading of zero)?
On the floor of a lift moving upwards with
uniform velocity.
(Radius of the Earth = 6.4  10 m .)
6
A.
(1), (2) and (3)
A.
2.4  10 12 rad s 1
B.
(1) and (2) only
C.
(2) and (3) only
B.
1.6  10 6 rad s 1
D.
(1) only
E.
(3) only
C.
1.3  10 3 rad s 1
D.
8.0  10 2 rad s 1
An object of mass m is released from a spacecraft
E.
6.4  10 5 rad s 1
which has radius R and mass M. On reaching the
5.
(92-I-5)
at a distance 3 R from the centre of the Earth
Earth’s surface, the increase in kinetic energy of
the object is
3.
(89-I-12)
Two points X and Y are at distances a and 2a from
the centre of the Earth. The gravitational potential
at X is
 8 kJkg 1 . When a 1 kg mass is taken
from X to Y the work done on the mass is
A.
Gm M/(3 R)
B.
2 Gm M/(3 R)
C.
Gm M/(2 R)
D.
E.
Gm M/ R
2 Gm M/ R
AL-MC-Gravitation / p.2
6.
(93-I-10)
8.
The velocity of escape from the earth is
(93-I-12)
A communication satellite appears stationary
V0 . For a
vertically above an observer at the equator. The
planet with radius twice that of the earth and with
height of the satellite above the observer is
density three times that of the earth, the velocity of
3.6 10 7 m . Calculate the mass of the earth.
6
Given : Radius of the earth = 6.4  10 m
escape from the planet would be
Gravitational constant = 6.7 10
A.
B.
7.
11
Nm2 kg 2
3V0 / 2
2V0
A.
4.5  10 24 kg
C.
6V0
B.
5.0  1024 kg
D.
2 3V 0
C.
5.5  10 24 kg
E.
2 6V0
D.
6.0  10 24 kg
E.
6.5  10 24 kg
(93-I-11)
For planets or satellites in circular orbits around a
celestial body such as the sun or the earth, the
9.
(94-IIA-11)
period T is related to the radius of orbit r by
Two satellites A and B of the same mass are
Kepler’s 3 rd Law T  kr
constant.
moving in circular orbits round the earth. The
2
3
where k is a
Which of the following statements concerning the
constant k is correct?
radius of A’s orbit is r and that of B’s orbit is 2r.
Their total mechanical energies are
E A and E B
respectively. Which of the following descriptions
A.
It is a dimensionless constant whose
value is not affected by the choice of
units.
B.
It is a universal constant whose value
depends on the choice of units.
D.
It would have a certain value for the
earth moving around the sun, but a
different value for another planet
moving around the sun.
E.
E A and E B is correctly? (Gravitational
potential energy is taken to be zero at infinity)
It is a universal constant whose value
is not affected by the choice of units.
C.
about
It would have a certain value for all
planets moving around the sun, but a
different value for all satellites moving
around the earth.
A.
E A > 0 and E B = 2 E A
B.
E A > 0 and E B = 1/2 E A
C.
E A > 0 and E B = -2 E A
D.
E A < 0 and E B = 2 E A
E.
E A < 0 and E B = 1/2 E A
AL-MC-Gravitation / p.3
10.
(95-IIA-10)
12.
(96-IIA-2)
In which of the following cases is the resultant
force on the object zero?
The figure shows a satellite S moving round a
(1)
a satellite moving round the earth
planet P in an elliptical orbit. Which of the
(2)
a feather falling freely in a vacuum cylinder
following statements is/are correct?
in a laboratory
(3)
(1)
The speed of the satellite at A is faster than
a gas bubble rising with terminal velocity in
water
when it is at B.
(2)
(3)
11.
The angular momentum of the satellite about
A.
(1) only
P is the same when it is at position A and B.
B.
(3) only
The total mechanical energy of the satellite is
C.
(1) and (2) only
the same at positions A and B.
D.
(2) and (3) only
E.
(1), (2) and (3)
A.
(1) only
B.
(3) only
C.
(1) and (2) only
Two satellites of the same mass travel around the
D.
(2) and (3) only
earth in circular orbits of different radii. The
E.
(1), (2) and (3)
satellite in the orbit with smaller radius has
13.
(96-IIA-3)
(95-IIA-11)
A.
a greater speed.
On a certain planet, an object is thrown vertically
B.
a longer period.
C.
a smaller acceleration towards the
upwards with an initial velocity of
v1 and it
earth’s centre.
returns to the ground after time t. If the velocity of
escape from the planet is
D.
a greater angular momentum about the
earth’s centre.
v2 , find the radius of the
E.
planet.
a greater sum of gravitational potential
energy and kinetic energy.
2
A.
2v1 t
v2
2
B.
4v1 t
v2
2
C.
2v 2 t
v1
D.
v2 t
4v1
2
2
E.
v2 t
2v1
14.
(97-IIA-10)
A low-altitude satellite near the earth’s surface has
1
a speed of 7.90 km s
. The radius of the earth is
about 4 times that of the moon and the ratio of the
average density of the earth to that of the moon is
about 5 : 4. The speed of a low-altitude satellite
near the moon’s surface would be
A.
1.77 km s
B.
2.21 km s
C.
2.47 km s
D.
3.57 km s
E.
4.42 km s
1
1
1
1
1
AL-MC-Gravitation / p.4
15. (98-IIA-17)
18.
(01-IIA-19)
The mass ratio of the earth and the moon is 81:1
Kepler discovered that the line joining the Sun and
and the earth-moon separation is 3.8  10 m. At
which position between the earth and the moon is
a revolving planet sweeps out equal areas in equal
the gravitational potential at a maximum? (Ignore all
explains this phenomenon is
8
times. The physical law which most directly
other planets.)
A.
B.
C.
D.
E.
A.
Newton’s first law of motion.
On the surface of the earth
B.
Newton’s third law of motion.
3.4  10 m from the earth
1.9  10 8 m from the earth
0.4  10 8 m from the earth
C.
Newton’s law of universal gravitation.
D.
conservation of angular momentum.
E.
conservation of energy.
8
On the surface of the moon
19.
16.
(99-IIA-18)
Due to air resistance, changes may occur to a
Which of the following statements about a
satellite orbiting the earth (assuming nearly
communication satellite in parking orbit above the
circular orbit). Which of the changes below is
earth’s surface is incorrect?
incorrect?
A.
It is accelerating towards the center of
the earth at all times.
B.
It must be in circular orbit above
A. The total mechanical energy of the
the
satellite will decrease.
earth’s equator.
C.
B. The angular momentum of the satellite
about the earth’s centre will decrease
It is always vertically above the same
place in the earth’s surface.
D.
C. The linear speed of the satellite will
It must be rotating in the same sense
increase.
and with the same angular speed as the
D. The time needed for the satellite to
earth.
E.
to its kinetic energy.
(00-IIA-9)
X and Y are two planets. Each of them has a
low-altitude satellite revolving in a circular orbit
close to the planet. If the two satellites are
observed to have the same period, then X and Y
must have nearly the same
A.
mass.
B.
average density.
C.
radius.
D.
acceleration due to gravity at the
planet’s surface.
E.
complete one revolution will increase.
It is at a height where its gravitational
potential energy is numerically equal
17.
(02-IIA-12)
gravitational potential at the planet’s
surface.
20.
(04-IIA-7)
A planet has a diameter 2 times that of the
earth and a mass 3 times that of the earth.
What is the approximate gravitational
field strength, in N kg-1, on the planet’s
surface?
A. 7.5
B. 10
C. 15
D. 30