CPP

IIT-JEE
CPP-1 Class - XII-CSO

GRAVITATION
1. The potential energy of gravitational interaction of a point mass m and a thin uniform rod of mass M and length
l, if they are located along a straight line at a distance a from each other is :
GMm al  1 1 
(A) U = – loge   (B) U = GMm   
a  a   a a l 

GMm al  GMm

(C) U = – loge   (D) U = –
l  a  a

2. Two air bubbles in water will behave as they :

(A) Attract each other (B) Repel each other
(C) Do not exert any force on each other
(D) May attract or repel depending upon the distance between them
3. Which of the following statements is/are not true about Newton’s law of gravitational force ?
(A) It is a two body interaction (B) It expresses the force between two point masses
(C) It depends on the medium between the particles (D) It is not valid for interatomic distance
4. Two tunnels are dug from one side of the earth’s surface to the other side, one along a diameter and the other
along a chord. Now two particles are dropped from one end of each of the tunnels. Both the particles oscillate
simple harmonically along the tunnels. Let T1 and T2 be the time periods and v1 and v2 be the maximum speed of
the particles in the two tunnels. Then :
(A) T1 = T2 (B) T1 > T2 (C) v1 = v2 (D) v1 > v2

5. Suppose, the acceleration due to gravity at the earth’s surface is 10 m/s2 and Weight

at the surface of Mars it is 4.0 m/s2. A 60 kg passenger goes from the earth to
600 N
the Mars in a spaceship moving with a constant velocity. Neglect all other A
objects in the sky. Which part of figure best represents the weight (net
gravitational force) of the passenger as a function of time : 240 N
B
(A) A
(B) B
C
(C) C D t0 Time
(D) D
6. The planet with radii R1, R2 have densities 1, 2 respectively. Their atmospheric pressures are p1, p2 respectively.
Therefore, the ratio of masses of their atmospheres, neglecting variation of g within the limits of atmosphere, is :
(A) p1 R2 1 / p2 R1 2 (B) p1 R2 2 / p2 R1 1 (C) p1 R1 1 / p2 R2 2 (D) p1 R1 2 / p2 R2 1
B
7. Two astronauts of equal mass are located at the points A and B at opposite ends of Spacecraft
a spacecraft near the earth as shown in the figure : A
(A) The centre of mass of two astronauts is at the mid-point of the line joining them
(B) The centre of gravity of two astronauts is at the mid-point of the line joining them
(C) The centre of gravity of two astronauts is closer to point A than to the point B
(D) The centre of gravity of two astronauts is closer to point B than to the point A Earth

 
8. Let S be an imaginary closed surface enclosing mass m. Let dS be an element of area on S, the direction of dS
   
being outward from S. Let E be the gravitational intensity at dS . We define  = E · dS , the integration being
carried out over the entire surface S :
(A)  = – Gm (B)  = – 4Gm

ANSWERS
1. (C) 2. (B) 3. (C,D) 4. (A,D) 5. (C) 6. (D) 7. (A,C) 8. (B)

FIITJEE Page 1
 CPP
IIT-JEE
CPP-2 Class - XII-CSO

GRAVITATION
y
1. A solid sphere of uniform density and radius 4 units is located with its centre at the
origin O. Two spheres of equal radii 1 unit with their centres at A (– 2, 0, 0) and B (2, 0,
0) respectively are taken out of the solid leaving behind cavities as shown in figure.
Then : x
A O B
(A) The gravitational field due to this object at origin is zero
(B) The gravitational field at the point B (2, 0, 0) is zero
(C) The gravitational potential is the same at all points on the circle y2 + z2 = 36
z
(D) The gravitational potential is the same at all points on the circle y2 + z2 = 4
k
2. Consider an attractive central force of the form F (r) = – n , k is a constant. For a stable circular orbit to exist :
r
(A) n = 2 (B) n < 3 (C) n > 3 (D) n = – 1
3. A tunnel is dug along a chord of the earth at a perpendicular distance R/2 from the earth's centre. The wall of the
tunnel may be assumed to be frictionless. A particle is released from one end of the tunnel. The pressing force by
the particle on the wall, and the acceleration of the particle varies with x (distance of the particle from the centre)
according to :
Acceleration

Acceleration
Pressing Force

Pressing Force

(A) (B) (C) (D)

x = R/2 x=R x x = R/2 x=R x x = R/2 x=R x x = R/2 x=R

4. Let g be the acceleration due to gravity at earth’s surface and K be the rotational kinetic energy of the earth.
Suppose the earth’s radius decreases by 2% keeping all other quantities same, then :
(A) g decreases by 2% and K decreases by 4% (B) g decreases by 4% and K increases by 2%
(C) g increases by 4% and K increases by 4% (D) g decreases by 4% and K increases by 4%
m
5. A thin spherical shell of mass M and radius R has a small hole. A particle of
mass m is released at the mouth of the hole. Then :
(A) The particle will execute simple harmonic motion inside the shell
(B) The particle will oscillate inside the shell, but the oscillations are not simple
harmonic R
M
(C) The particle will not oscillate, but the speed of the particle will go on increasing
(D) None of these

6. A spherical shell is cut into two pieces along a chord as shown in figure. If I denote the
gravitational field strength, then for points P and Q :
Q
(A) IP > IQ
P
(B) IP < IQ
(C) IP = IQ = 0
(D) IP = IQ  0

7. The gravitational field in a region is given by I = (2 i^ + 3 j^ ) N/kg. What is the work done in moving a particle
1
from (1m, 1m) to  2m, m  along the line 3y + 2x = 5 ?
 3 
(A) Zero (B) + 20 J (C) – 15 J (D) + 18 J
* * * * *
ANSWERS
1. (A,C,D) 2. (A,B,D) 3. (B,C) 4. (C) 5. (D) 6. (D) 7. (A)

FIITJEE Page 2
 CPP
IIT-JEE
CPP-3 Class - XII-CSO

GRAVITATION
1. A straight rod of length l extends from x =  to x = l + . If the mass per unit length is (a + bx2). The gravitational
force it exerts on a point mass m placed at x = 0 is given by : y

  Gm (a  bx 2 )
(A) Gm  a  1  1   bl  (B) m x
     l   l2  l

 1 1     1 1 
(C) Gm       bl  (D) Gm  a     bl 
  a a  l       l    P
a

d b
2. Figure show a hemispherical shell having uniform mass density. The direction of c
gravitational field intensity at point P will be along :
(A) a (B) b
(C) c (D) d

3. A sphere of mass M and radius R2 has a concentric cavity of radius R1 as shown in

R1
figure. The force F exerted by the sphere on a particle of mass m located at a distance r R2
from the centre of sphere varies as (0  r ) :
F F F F

(A) (B) (C) (D)

r r r r

4. The distance from the surface of the earth at which the acceleration due to gravity is the same below and above the
surface of the earth :
 5 1  ( 5  1) Re
(A) ( 5  1) Re (B)   Re (C) (D) ( 5  1) Re
 2  2

5. Consider a uniform shell of mass M and radius R. Suppose a point mass m is placed inside shell as shown. Point
mass lies at distances r1 and r2 from two opposite surfaces shown. Suppose dM1 and dM2 be the masses of surface
elements on the two sides and they attract the particle with forces dF1 and dF2 respectively. Then which one of the
following is true. (Consider  to be infinitesimal small angle) : M

dF1 r22 dF r
(A)  (B) dF1  r2 r1
dF2 r12 2 1 r2 dM1
r1

dF1 r12
(C) dF1 = dF2 (D)  r2
dF2 r22 dM2

6. Two blocks of masses m each are hung from a balance. The scale pan A is at height
H1 whereas scale pan B is at height H2. Net torque acting on the rod of pan, will l/2 l/2
be (length of the rod is l and H1 & H2 are << R) (H1 > H2) : A m m B
 1  2H1  mg
(A) mg  l (B) (H1 – H2) l
 R  R H1 H2

2mg H 2 H1
(C) (H1 + H2) l (D) 2mg l
R H1  H 2

ANSWERS
* * * * *
1. (A) 2. (C) 3. (B) 4. (C) 5. (C) 6. (B)
FIITJEE Page 3
 CPP
IIT-JEE
CPP-4 Class - XII-CSO

GRAVITATION
g' = 5 ms–2

1. If acceleration due to gravity is 10 ms–2 then let acceleration due to gravitational

acceleration at another planet of our solar system be 5 ms–2. An astronaut weighing
50 kg on earth goes to this planet in a spaceship with a constant velocity. The weight
of the astronaut with time of flight is roughly given by :

g' = 10 ms–2
Weight

Weight

Weight

Weight
500 N 500 N 500 N 500 N

(A) (B) (C) (D)

250 N 250 N 250 N 250 N

Time Time Time Time

2. Suppose a smooth tunnel is dug along a straight line joining two points on the surface of the earth and a particle
is dropped from rest at its one end. Assume that mass of earth is uniformly distributed over its Volume. Then
(A) Acceleration of the particle will be proportional to its distance from midpoint of the tunnel.
GM e
(B) The particle will emerge from the other end with velocity where Me and Re are earth’s mass and radius
2 Re
respectively,
(C) The particle will come to rest at centre of the tunnel because at this position, particle is closest to earth centre.
(D) Potential energy of the particle will be equal to zero at centre of tunnel if it is along a diametre.
3. Two identical thin rings each of radius R are coaxially placed at a distance R. If the rings have a uniform mass
distribution and each has mass m1 and m2 respectively, then the work done in moving a mass m from centre of one
ring to that of the other is :
GM ( M 1  M 2 )( 2  1) GM 2( M1  M 2 ) GMM1 ( 2  1)
(A) Zero (B) (C) (D)
2R R M2R

4. A point P (R 3 , 0, 0) lies on the axis of a ring of mass M and radius R. The ring is located in y-z plane with its
centre at origin O. A small particle of mass m starts from P and reaches O under gravitational attraction only. Its
speed at O will be :
GM Gm GM Gm
(A) (B) (C) (D)
R R 2R 2R
5. If g is the acceleration due to gravity on the earth's surface, the change 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) mgR/2 (B) 2mgR (C) mgR (D) –mgR
6. With what minimum speed should m be projected from point C in presence of Vmin
two fixed masses M each at A and B as shown in the figure such that mass m m 30º
C
should escape the gravitational attraction of A and B :

(A) 2GM (B) 2 2GM R

R R M
GM A R R B
(C) 2 (D) 2 2 GM
R R
ANSWERS
* * * * *
1. (A) 2. (A) 3. (B) 4. (A) 5. (A) 6. (B)
FIITJEE Page 4
 CPP
IIT-JEE
CPP-5 Class - XII-CSO

GRAVITATION
1. Three particles of mass M each are lying on the corners of an equilateral triangle M
of side l. If the length of each side of the triangle is increased to twice :
3GM 2
(A) P.E. on increasing the length is
2l
2l 2l
3GM 2 l l
(B) Work done is
2l
GM 2 l
(C) Work done is
l M M
1.5 GM 2 2l
(D) P.E. on increasing the length is
l
2. Two bodies of masses m and M are placed a distance d apart. The gravitational potential at the position where the
gravitational field due to them is zero is V :
G Gm Gm G
(A) V = – (m + M) (B) V = – (C) V = – (D) V = – ( m + M )2
d d d d
3. Distance between the centres of two stars is '5 a'. The masses of these stars are M & 81 M and their radii are 'a'
each. A body of mass 'm' is fired straight from the surface of the heavier star towards the lighter star. What should
be its minimum initial speed to reach the surface of the smaller star ? Obtain the expression in terms of G, M & a.
(Assume both the stars to be solid spheres with uniform mass distribution)
120 GM 675 GM 117 GM
(A) (B) (C) (D) None of these
a 28 a a
4. If a body is projected with speed lesser than escape velocity :
(A) The body can reach a certain height and may fall down following a straight line path
(B) The body can reach a certain height and may fall down following a parabolic path
(C) The body may orbit the earth in a circular orbit
(D) The body may orbit the earth in an elliptical orbit
5. Two identical trains P and Q move with equal speeds on parallel tracks along the equator. P moves from east to
west and Q from west to east :
(A) Train P exerts greater force on track (B) Train Q exerts greater force on track
(C) Both exert equal force on track (D) Data is insufficient to arrive at a conclusion
6. Consider a planet moving in an elliptical orbit around the sun. The work done on the planet by the gravitational
force of the sun :
(A) Is zero in every small part of the orbit (B) Is zero in some parts of the orbit
(C) Is zero in one complete revolution (D) Is zero in no part of the motion
7. Let gravitation field in a space be given as E = – (k/r). If the reference point is at di where potential is Vi then
relation for potential is :
1 r r r V
(A) V = k log V + 0 (B) V = k log + Vi (C) V = log + kVi (D) V = log + i
i di di di k
8. A particle is placed in a field characterised by a value of gravitational potential given by V = – kxy, where k is a

constant. If E g is the gravitational field then,
 
(A) E g = k (x iˆ + y ĵ ) and is conservative in nature (B) E g = k (y iˆ + x ĵ ) and is conservative in nature
 
(C) E g = k (x iˆ + y ĵ ) and is non-conservative in nature (D) E g = k (y iˆ + x ĵ ) and is non-conservative in nature
* * * * *
ANSWERS
1. (A,B) 2. (D) 3. (A) 4. (A,B,C,D) 5. (A) 6. (B,C) 7. (B) 8. (B)

FIITJEE Page 5
 CPP
IIT-JEE
CPP-6 Class - XII-CSO

GRAVITATION
1. A very very large number of particles of same mass m are kept at horizontal distances of 1 m, 2 m, 4 m, 8 m and so
on from (0, 0) point. The total gravitational potential at this point is :
(A) – 8G m (B) – 3G m (C) – 4G m (D) – 2G m
2. The gravitational potential of two homogeneous spherical shells A and B of same surface density at their respective
centres are in the ratio 3 : 4. If the two shells coalesce into single one such that surface mass density remains same,
Then the ratio of potential at an internal point of the new shell to shell A is equal to :
(A) 3 : 2 (B) 4 : 3 (C) 5 : 3 (D) 3 : 5
3. A particle released at a large distance from the planet reaches the planet only under gravitational attraction and
passes through a smooth tunnel through its centre. If ve is the escape velocity of a body from the planet then the
particle’s speed at the centre of the planet is :
(A) ve (B) 1.5ve (C) 1.5 ve (D) 2 ve

4. Consider a circular disc of mass M, radius R with surface mass density . The gravitational potential due to the disc
at a point P lying on its axis at distance r from the centre is :
r r
(A) – 2Gr (B) – 4Gr (C) – 2Gr 1  
 (D) – 4Gr  1  

 r2  R2   r2  R2 

5. The curve for potential energy (U) and kinetic energy (Ek) of a two particle Ek
system are shown in figure. At what points the system will be bound ?
Energy
(A) Only at point D O
A B C D r
(B) Only at point A
(C) At point D and A U
(D) At points A, B and C

6. Two small satellites move in circular orbits around the earth, at distances r and r + r from the centre of the earth.
Their time periods of rotation are T and T. (r << r, T << T) :
3 r 3 r 2 r r
(A) T = T (B) T = – T (C) T = T (D) T = T
2 r 2 r 3 r r
7. The maximum and minimum distance of the earth from the sun are r1 and r2 respectively :
(A) The time period of revolution of earth is proportional to (r1 + r2)3/2
(B) The period of revolution is proportional to (r1 – r3)3/2
(C) The distance of earth from the sun, when it is at a position axis and passing through the sun in its sun in its
orbit, is (2r1r2)/(r1 + r2)
(D) The distance of earth from the sun, when it is at a position perpendicular to the principal axis and passing
through the sun in its orbit, is (r1 + r2)/2
8. A satellite of mass m orbits the earth in an elliptical orbit having aphelion distance ra and perihelion distance rp.
ra  rp
The period of the orbit is T. The semi-major and semi-minor axes of the ellipse are and rp ra respectively..
2
The angular momentum of the satellite is :
m(ra  rp ) ra rp 2m(ra  rp ) ra rp m(ra  rp ) ra rp m(ra  rp ) ra rp
(A ) (B) (C) (D)
T T 2T 4T
* * * * *

ANSWERS
1. (D) 2. (C) 3. (B) 4. (C) 5.(D) 6. (A) 7.(A, C) 8.(A)

FIITJEE Page 6
 CPP
IIT-JEE
CPP-7 Class - XII-CSO

GRAVITATION
1. A satellite is orbiting round the earth’s surface in an orbit as close as possible to the surface of the earth.
(A) The time period of revolution of satellite is independent of its mass and is maximum.
(B) The orbital speed of satellite is maximum.
(C) The Kinetic energy of the satellite is minimum.
(D) The total energy of the “earth plus satellite” system is maximum.

2. The escape velocity for a planet is ve. A particle is projected from its surface with a speed v. For this particle to
move as a satellite around the planet :
v v v v
(A) e  v  ve (B) e  v  ve (C) ve  v  2ve (D) e  v  2e
2 2 2

3. The orbital period of revolution of a planet round the sun is T0. Suppose we make a model of Solar system scaled
down in the ratio  but of materials of the same mean density as the actual material of planet and the sun has. The
new orbital period is :
(A) T0 (B) 2T0 (C) 3T0 (D) T0

4. A geostationary satellite S is stationed above a point P on the equator. A particle is fired from S directly towards P :
(A) With respect to the axis of rotation of the earth, P and S have the same angular velocity but different linear
velocities.
(B) The particle will hit P
(C) The particle will hit the equator east of P
(D) The particle will hit the equator west of P

5. A planet of mass m is moving around the sun in an elliptical orbit of semi-major axis a :
(A) The total mechanical energy of the planet is varying periodically with time
GmM s
(B) The total mechanical energy of the planet is constant and equals – , Ms is mass of sun
2a
GmM s
(C) Total mechanical energy of the planet is constant and equals – , Ms is mass of sun
a
(D) Data is insufficient to arrive at a conclusion

6. Imagine a light planet revolving around a very massive star in a circular orbit of radius R with a period of revolution
T. If the gravitational force of attraction between the planet and the star is proportional to R–5/2, then T 2  :
(A) R3 (B) R7/2 (C) R5/2 (D) R3/2

7. An astronaut inside an earth satellite experiences weightlessness because :

(A) No external force is acting on him (B) He is falling freely
(C) No reaction is exerted by floor of the satellite (D) He is far away from earth

8. For a satellite to orbit around the earth, which of the following must be true ?
(A) It must be above the equator at some time
(B) It cannot pass over the poles at any time
(C) Its height above the surface cannot exceed 36,000 km
(D) Its period of rotation must be > 2 R/g

******
ANSWERS
1. (A,B,C) 2. (B) 3. (D) 4. (A, C) 5.(B) 6. (B) 7.(B, C) 8.(A,D)

FIITJEE Page 7
 CPP
IIT-JEE
CPP-8 Class - XII-CSO

GRAVITATION
1. A satellite close to the earth is in orbit above the equator with a period of rotation of 1.5 hours. If it is above a point
P on the equator at some time, it will be above P again after time :
(A) 1.5 hours (B) 1.6 hours if it is rotating from west to east
(C) 24/17 hours if it is rotating from west to east (D) 24/17 hours if it is rotating from east to west

2. For a satellite to be geostationary, which of the following are essential conditions ?

(A) It must always be stationed above the equator (B) It must rotate from west to east
(C) It must be about 36,000 km above the earth (D) Its orbit must be circular, and not elliptical

3. A planet revolves around the sun in an elliptical orbit of eccentricity e. If T is the time period of the planet, then the
time spent by the planet between the ends of the minor axis close to the sun is :
1 e  T. e e  T
(A) T    (B) (C)   1 T (D)
 4 2     e

4. An artificial satellite is in a circular orbit around the earth. The universal gravitational constant starts decreasing at
time t = 0, at a constant rate with respect to time t. Then the satellite has its :
(A) Path gradually spiralling out, away from the centre of the earth
(B) Path gradually spiralling in, towards the centre of the earth
(C) Angular momentum about the centre of the earth remains constant
(D) Potential energy increases

5. A satellite is revolving round the earth in an elliptical orbit :

(A) Gravitational force exerted by earth is equal to centripetal force at some points only
(B) Power associated with gravitational force is zero at every point
(C) Work done by gravitational force is zero in some small parts of the orbit
(D) At some point, magnitude of gravitational force is greater than that of centripetal force

6. A planet orbits the sun, its speed :

(A) Increases in going from aphelion to perihelion (B) Decreases in gong from perihelion to aphelion
(C) Remains same throughout (D) Varies at random

7. The ratio of Earth’s orbital angular momentum (about the Sun) to its mass is 4.4 × 1015 m2 s–1. The area enclosed
by the earth’s orbit is approximately :
(A) 1 × 1022 m2 (B) 3 × 1022 m2 (C) 5 × 1022 m2 (D) 7 × 1022 m2

8. A satellite of mass m is orbiting just above the surface of earth :

(A) Its orbital speed v0 = 2 gR (B) Its orbital speed v0 = gR
(C) Its time period is 2 R / g (D) Its time period is approximately 84.6 minutes
(R = Radius of earth and g = acceleration due to gravity on earth’s surface)

*****

ANSWERS
1. (B,D) 2. (A,B,C,D) 3. (A) 4. (A,C,D) 5.(A,C,D) 6. (A,B) 7.(D) 8.(B,C,D)

FIITJEE Page 8
 CPP
IIT-JEE
CPP-9 Class - XII-CSO

GRAVITATION
1. Let v, T, L, K and r denote the speed, time period, angular momentum, kinetic energy and radius of satellite in a
circular orbit, then :
(A) v  r–1 (B) L  r1/2 (C) T  r3/2 (D) K  r–2
2. If the earth suddenly stopped in its orbit (assume orbit to be circular) the time that would elapse before it falls into
the sun is :
1 1 1 1
(A) T (B) T (C) T (D) T
2 2 2 4 2 8 2

3. Periodic-time of satellite revolving around the earth is-( is density of earth) :

1 1
(A) Proportional to (B) Proportional to (C) Proportional  (D) Does not depend on 
 

4. An artificial satellite of the earth releases a package. If air resistance is neglected the point where the package will
hit (with respect to the position at the time of release) Will be :
(A) Ahead (B) Exactly below
(C) Behind (D) It will never reach the earth
5. A satellite in earth orbit experience a small drag force as it enters the earth' atmosphere. Two students were asked
consequence of the :
Student-A : The satellite would slow down as, it spirals towards earth due to work of frictional force.
Student-B : The satellite speed up due to earths gravitational pull as it spirals towards earth.
(A) A is correct, B is wrong (B) B is correct, A is wrong
(C) Both are correct (D) Both are wrong
6. A body of superdense material with mass twice the mass of earth but size very small compared to the size of earth
starts from rest from h << R above the earth’s surface. It reaches earth in time t :
h 2h 2h 4h
(A) t = g (B) t = (C) t = (D) t =
g 3g 3g

7. A satellite of mass 5 M orbits the earth in a circular orbit. At one point in its orbit, the satellite explodes into two
pieces, one of mass M and the other of mass 4 M. After the explosion the mass M ends up travelling in the same
circular orbit, but in opposite direction. After explosion the mass 4 M is in :
(A) Bound orbit
(B) Unbound orbit
(C) Partially bound orbit
(D) Data is insufficient to determine the nature of the orbit
8. Two particles having masses m1 and m2 respectively attract each other, according to the Newton’s law of gravitation.
Initially they are at rest and on infinite distance apart :
Gm1m2
(A) The work done in moving these two to a distance r apart is 
r
(B) The work done in moving them r distance apart is Gm1m2/2r
2G(m1  m2 )
(C) The velocity of approach of the particles at a separation r is
r
(D) The velocity of approach is G (m1 + m2)/r

******
ANSWERS
1. (B,C) 2. (C) 3. (B) 4. (D) 5.(B) 6. (C) 7.(B) 8.(A,C)

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 CPP
IIT-JEE
CPP-10 Class - XII-CSO

GRAVITATION
1. Suppose our planet, the earth, suddenly shrinks in size, still remaining perfectly spherical with mass remaining
unchanged, then :
(A) The duration of the day will decrease
(B) The kinetic energy of rotation about its own axis will increase
(C) The duration of the year will remain unchanged
(D) None of these

2. Three identical stars of mass M are located at the verticals of an equilateral triangle with side L. The speed at which
they will move if they all revolve under the influence of one another's gravitational force in a circular orbit
circumscribing the triangle while still preserving the equilateral triangle :

2GM GM GM
(A) (B) (C) 2 (D) Not possible at all
L L L

3. Four similar particles of mass m are orbiting in a circle of radius r in the same direction because of their mutual
gravitational attractive force. Velocity of a particle is given by :
m
1
 Gm  1  2 2  2 Gm
(A)    (B) 3
 r  4   r
m
r
m
1
Gm  1 Gm  1  2 2  2
(C)
r 
1 2 2  (D) 
2 r  2 
  
m

4. A double star is system of two stars rotating about their centre of mass only under their mutual gravitational
attraction. Let the stars have masses m and 2 m and let their separation be l. Their time period of rotation about
their centre of mass will be proportional to :
(A) l3/2 (B) l (C) m1/2 (D) m–1/2

******

ANSWERS
1. (A,B,C) 2. (B) 3. (A) 4. (A,D)

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