Gravitation
Q.1 Two particles of mass m and M are initially at rest and infinitely separated from each other. Due to gravitational attraction they approach each other. Their relative velocity of approach at a separation r between them is
(a) [Gr /M + m]1/2 (b) [2G(M + m)/r]1/2
(c) 2G (M + m)1/2 (d) 2Gr(M + m)
Q.2 Four particles, each of mass 1kg are at the corners of a square of side 1m. The work which must be done to remove on of the particle of infinity is
(a) 2Ö2G (b) (2Ö2+1)/Ö2 G
(c) (2Ö2+1) G (d) 3G
Q.3 Three particles of mass m each are placed at the three corners of an equilateral triangle of side a. The work which should be done to increase the sides of the triangle to 2a is
(a) 3Gm2 / a (b) 3Gm2 / 2a
(c) Gm2 / 2a (d) 3Gm / 2a
Q.4 The gravitational force of attraction on a unit mass particle placed at a distance of r from the centre and on the axis of a uniform ring of mass M and radius R is
(a) GM/r2 (b) GM/R2
(c) GM r/ (r2+R2)3/2 (d) GM/ (r2+R2)
Q.5 A particle of mass 1kg is placed at a distance of 4m from the centre and on the axis of a uniform ring of mass 5kg and radius 3m. The work done to increase the distance of the particle from 4m to 3Ö3m in joules is
(a) G/3 (b) G/4
(c) G/5 (d) G/6
Q.6 Inside a uniform spherical shell
(a) the gravitational potential is zero
(b) the gravitational field is zero
(c) the gravitational potential is same everywhere
(d) the gravitational field is proportional to distance from the centre.
Q.7 If the radius of the earth is reduced by 1% keeping its mass unchanged, the change in the acceleration due to gravity is
(a) 2% increase (b) 1% increase
(c) 2% decrease (d) 1% decrease
Q.8 A star suddenly shrinks and its density becomes 109 times its original value. The value of acceleration due to gravity on its surface will increase by a factor of
(a) 10-9 (b) 10-6 (c) 106 (d) 109
Q.9 The radius of the earth’s orbit is 6400km and g = 10m/s2. In order that a body of 5kg weighs zero at equator, the angular speed, in radians, of the earth should be
(a) 1/80 (b) 1/400 (c) 1/800 (d) 1/1600
Q.10 The weight of a body as measured by a spring balance in a train at rest is W0, when the train begins to move with velocity v around the equator from west to east and the earth is rotating with angular velocity w, then the weight shown by the spring balance is
(a) W0 (b) W0 (1+2vw/g)
(c) W0 (1-2vw/g) (d) W0 (1+v2/g)
Q.11 Two identical trains are moving on rails along the equator on the earth in opposite directions with the same speed. The train A is moving towards east and the train B towards west. The pressure exerted on the rails will be
(a) same due to both (b) zero due to both
(c) more for train A (d) more for train B
Q.12 If g be the acceleration due to gravity of the earth’s surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is
(a) ½ mgR (b) 2mgR (c) mgR (d) ¼ mgR
Q.13 Consider two planets with the same density but radii R1 and R2. The ratio of escape velocities v1/v2 from their respective surfaces will be
(a) (R2/R1)2 (b) R2/R1 (c) R1/ R2 (d) (R1/ R2)2
Q.14 A satellite is moving round the earth. In order to make it move to infinity, its velocity must be increased by
(a) 20% (b) 41.4% (c) 82.8% (d) 100%
Q.15 Two identical satellites revolving in the same orbit around the earth in the opposite directions make an inelastic collision so that wreckage form one piece, then this piece of tangled material
(a) will move in an orbit of half the original radius
(b) will move in an orbit of one-fourth the radius
(c) will escape to infinity
(d) falls directly on the earth
Q.16 A planet moves round the sun. At a point P it is closest to the sun at a distance d1and has a speed v1. At another point Q, when it is farthest from the sun at a distance d2, its speed will be
(a) d12v1/d22 (b) d2v1/d1 (c) d1v1/d2 (d) d22v1/d12
Q.17 Consider the following periodic motions-
(a) A simple pendulum of infinite length will bob near the earth’s surface
(b) A ball oscillating in a tunnel dug through the earth
(c) A satellite revolving round the earth close to the earth’s surface
(d) A satellite revolving round the earth at a height equal to the earth’s radius.
Which of the above periodic motions have the same period
(a) 1, 2, 3 (b) 2, 3, 4 (c) 3, 4, 1 (d) 4, 3, 2
Q.18 The ratio of the kinetic energy required to give to the satellite to escape earth’s gravitational field to the kinetic energy required to put the satellite in a circular orbit close to the earth’s surface is
(a) 1 (b) 2 (c) ½ (d) ¥
Q.19 A satellite of mass m is revolving round the earth at a height R above the surface of the earth, where R is the radius of the earth. If g is the acceleration due to gravity at the surface of the earth, the kinetic energy of the satellite is
(a) ¼ mgR (b) ½ mgR (c) mgR (d) 2mgR
Q.20 The orbit velocity of an artificial satellite in a circular orbit just above the earth surface is v. The speed for another orbiting at an altitude of half the earth’s radius is
(a) 3/2 v (b) [Ö3/2]v (c) [Ö2/3]v (d) 2/3v
Q.21 A satellite is orbiting the earth in a circular orbit of radius r. Its
(a) kinetic energy varies as 1/r (b) linear momentum varies as 1/r
(c) angular momentum varies as 1/Ör (d) frequency varies as 1/Ör3
Q.22 Suppose the law of gravitational attraction suddenly changes and follows inverse cube law i.e., F a 1/r3, then
(a) Kepler’s law of areas still holds (b) Kepler’s law of period still holds
(c) The laws of areas as well as the law of periods still hold
(d) Neither the low of areas nor the law of periods remains valid.
Q.23 The eccentricity of the earth’s orbit is 0.0167. The ratio of its maximum speed in its orbit to its minimum speed is
(a) 2.507 (b) 1.033 (c) 8.324 (d) 1.000
Q.24 A satellite moves round a planet in an elliptical orbit. The maximum and minimum distance of the planet from the planet are r1 and r2 respectively. The time period of the satellite is proportional to
(a) r13/2 (b) r23/2 (c) (r1+r2)3/2 (d) (r1-r2)3/2
Q.25 Two satellites A and B go around a planet P in circular orbits having radii 4R and R respectively. If the speed of satellite A is 3 v, the speed of satellite B would be
(a) 12 v (b) 6v (c) [4/3]v (d) (3/2)v
Q.26 If the distance between the earth and the sun were half at its present value, the number of days in a year would have been
(a) 64.5 (b) 129 (c) 182.5 (d) 730
Q.27 When the body is moving up, the acceleration due to gravity will be:
(a) Downward (b) Upward (c) Sideways (d) Nil
Q.28 At sea level the value of g is minimum at:
(a) The equator (b) 45° north latitude
(c) 45° south latitude (d) The pole
Q.29 As we go from the equator to the poles, the value of g :
(a) Remains the same (b) Decrease
(c) Increases
(d) Decrease up to a latitude of 45° and then increases
Q.30 The value of g will be 1% of its value at the surface of earth at a height of (Re = 6400 km)
(a) 6400 km (b) 57600 km (c) 2560 km (d) 64000 km
Answer Sheet
1.
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(b)
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2.
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(b)
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3.
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(b)
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4.
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(c)
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5.
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(d)
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6.
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(b), (c)
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7.
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(a)
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8.
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(c)
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9.
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(c)
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10.
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(c)
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11.
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(d)
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12.
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(a)
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13.
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(c)
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14.
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(b)
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15.
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(d)
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16.
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(c)
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17.
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(a)
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18.
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(a)
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19.
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(a)
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20.
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(c)
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21.
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(a), (b), (d)
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22.
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(a)
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23.
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(b)
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24.
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(c)
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25.
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(b)
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26.
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(b)
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27.
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(a)
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28.
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(a)
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29.
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(c)
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30.
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(b)
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Rotation
Motion
Q.1 Two
point masses (of mass m1
and m2) all joining by a
massless string of length r. The
moment of inertia of the system about an axis passing through the centre of
mass and perpendicular to the string is
(a) (m1 + m2) r2 (b) m1
m2 /m1 + m2 r2
(c) m1
/ m2(m1 + m2)
r2 (d) m2
/ m1 (m1+ m2)
r2
Q.2 A closed tube partly filled with water lies in a horizontal
plane. If the tube is rotated about a perpendicular bisector, the moment of
inertia of system
(a) increase (b) decrease
(c) remains constant (d) depends on sense of rotation
Q.3 A rod A B of mass
m and length is rotating in a
vertical plane about its fixed end A.
A particle of mass m is attached to
its other end B. If the velocity of
the particle when it is at the lowest position, its velocity is
(a) Ö9gl (b) Ö5gl (c) Ö4gl (d) Ö3gl
Q.4 A solid cylinder of mass m and radius r rolls down
an inclined plane of height h. The
friction of the energy which is transformed into rotational kinetic energy is
(a) ½ (b) 1/3 (c) ¼ (d) 2/3
Q.5 A disc of mass M
and radius R is rotating in a
horizontal plane about an axis passing through its centre and perpendicular to
it which angular velocity w.
Another disc of half the radius but double the mass is placed gently on the
first coaxially. The new angular velocity of the system will be
(a) 2/3w (b) 2/5w (c) 3/5w (d) 4/5w
Q.6 A particle moves with a constant velocity parallel to the
axis. Its angular momentum with respect to the origin
(a) is zero (b) remains constant
(c) goes on increasing (d) goes on decreasing
Q.7 A small object of mass m
is attached to a light string and made to rotate on a small frictionless table
in a circular path whose radius can be changed, by pulling the other end of the
string through the hole at the centre. If the initial and final values of the
radius of the orbit, speed and angular velocities of the object are r1, v1, w1 and r2, v2, w2 respectively, then
w2/w1 respectively
(a) r1
/ r2 (b) (r1 / r2)2 (c) ( r2 / r1)2 (d) r2 / r1
Q.8 A thin circular ring of mass M and radius R rotates
about its axis with a constant angular velocity w. Two equal masses, each of mass m are placed gently on to the ring. Now the angular velocity of the
ring is
(a) M / M + m
w (b) (M
+2 m) / M w
(c) (M -2 m) / (M +2 m) w (d) M /
(M +2 m) w
Q.9 A man standing on a horizontal turntable turning at a
certain angular frequency, with his arms folded has equal weights in his hands.
When he stretches his arms horizontally, the final kinetic energy of the system
is
(a) same as before
(b) less than
before because part of it is converted into potential energy
(c) less than before because part of it is
converted into heart
(d) greater than before because part of
potential energy is converted into kinetic energy
Q.10 A loaded truck has to take a sharp turn to the left. The
centre of gravity of the truck can be altered by shifting a concentrated load.
To avoid toppling, the load must be shifted
(a) up and left (b) down and left
(c) up and right (d) down and right
Q.11 A Ping-Pong ball is floating on the top of a vertical water
jet. In the vertical direction it is in the
(a) stable equilibrium (b) unstable equilibrium
(c) neutral equilibrium (d) equilibrium position
Q.12 A constant torque acting on a uniform circular wheel
changes its angular momentum from A0
to 4 A0 in 4 seconds. The
magnitude of this torque is
(a) 3A0/4
(b) 4A0 (c) A0 (d) 2A0
Q.13 For a system
to be in equilibrium, the torques acting on it must balance. This is true only
if the torques are taken about
(a)
The
centre of the system
(b)
the
centre of mass of the system
(c)
any
point on the system
(d)
any
point on the system or outside
Q.14 A uniform
horizontal metre scale of mass m is
suspended but two vertical strings attached to its two ends. A body of mass 2m is placed on the 75 cm mark. The
tensions in the two strings are in the ratio
(a) 1 : 2 (b)
1 : 3 (c) 2
: 3 (d) 3 : 4
Q.15 A
flywheel rotate with a uniform angular velocity increases from 20p rad/s to 40p
rad/s in 10seconds. How many rotations did it make in this period?
(a) 80 (b)
100 (c) 120 (d) 150
Q.16 When
a ceiling fan is switched on, it makes 10 rotations in the first 3 seconds. How
many rotations will it make in the next 3 seconds? (Assume uniform angular
acceleration)
(a) 10 (b) 20 (c) 30 (d) 40
Q.17 When
a ceiling fan is switched off, its angular velocity falls to half while it
makes 36 rotations. How many more rotations will it make before coming to rest?
(Assume uniform angular retardation)
(a) 36 (b) 24 (c) 18 (d)
12
Q.18 A
flywheel rotates about an axis. Due to friction at the axis, it experiences an
angular retardation proportional to its angular velocity. If its angular
velocity falls to half while it makes n
retardation. How many more rotations will it make before coming to rest ?
(a) 2n
(b) n (c) n/2 (d) n/3
Q.19 An
external device, e.g., an electric motor, supplies constant power to a rotating
system, e.g., a flywheel, through a torque t.
The angular velocity of the system is w.
Both t and w
are variable.
(a) w µ t (b) w µ 1/t (c) w µÖt (d) w µ1/ Öt
Q.20 The
radius of gyration of a thin disc of radius 4 cm about a diameter is
(a) 4 cm (b) 2Ö2 cm (c) 2 cm (d)
Ö2 cm
Q.21 The
radius of gyration of a solid sphere of radius r about a certain axis is r.
The distance of this axis from the centre of the sphere is
(a) r (b) 0.5r (c) Ö0.6r (d) Ö0.4r
Q.22 If
the radius of the earth becomes half of its present value, with its mass
remaining the same, the duration of one day will become
(a) 6h (b) 12h (c) 48 h (d)
96 h
Q.23 A
small ball strikes a stationary uniform rod, which is free to rotate, in
gravity- free space. The ball does not stick to the rod. The rod will rotate
about
(a) its centre
of mass
(b)
the
centre of mass of ‘rod plus ball’
(c)
the
point of impact of the ball on the rod
(d)
the
point about which the moment of inertia of the ‘rod plus ball’ is minimum
Q.24 A triangular frame in the form
of an equilateral triangle of side a is formed by bending a uniform thin bar of
length 3a and mass M. The moment of inertia of the frame about an axis passing
through the center of mass an perpendicular to its plane is
(a) ½ Ma2 (b) 1/3
Ma2 (c) 1/6 Ma2 (d) 1/12
Ma2
Q.25 Moment of
inertia of a uniform circular disc about a diameter is I. Its moment of inertia
about an axis perpendicular to its plane and passing through a point on its rim
will be :
(a) 5I (b) 3I (c)
6I (d)
4I
Q.26 Let l be the
moment of inertia of a uniform square plate about an axis AB that passes
through its centre and is parallel to two of its sides. CD is alone in the
plane of the plate that passes through the centre of the plate and makes an
angle q with AB. The moment of inertia
of the plate about the axis CD is then equal to
(a) I (b) I sin2 q
(c) I cos2 q (d) I cos2 (q/2)
Q.27 Two circular
discs are of the same thickness. The diameter of A is twice that of B. the
moment of inertia of A as compared to that of B is :
(a) twice as large (b) four times as large
(c) 8 times as large (d) 16 times as large
Q.28 Moment of inertia comes into play :
(a) In translatory motion (b) In rotatory motion
(a)
In
vibratory motion
(b)
When the
body is permanently at rest
Q.29 Moment
of inertia plays the same role in rotatory motion as in translatory motion is
played by :
(a) Velocity (b) Acceleration (c) Mass (d) Force
Q.30 The moment of
inertia of a body does not depend on
(a)
The
mass of the body
(b)
The
angular velocity of the body
(c)
The
axis of rotation of the body
(d)
The
distribution of the mass in the body
Answer Sheet
1.
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(b)
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2.
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(a)
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3.
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(a)
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4.
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(b)
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5.
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(a)
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6.
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(b)
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7.
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(b)
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8.
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(d)
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9.
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(b)
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10.
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(b)
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11.
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(a)
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12.
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(a)
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13.
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(d)
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14.
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(a)
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15.
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(d)
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16.
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(c)
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17.
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(d)
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18.
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(b)
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19.
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(b)
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20.
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(c)
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21.
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(c)
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22.
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(a)
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23.
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(a)
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24
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(c)
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25.
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(c)
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26.
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(a)
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27.
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(d)
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28.
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(b)
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29.
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(c)
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30.
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(b)
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