DC Pandey Solutions (JEE Advance): Gravitation | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


For JEE Advanced 
  Assertion and Reason  
Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : When two masses come closer, their gravitational potential energy decreases.  
  Reason : Two masses attract each other. 
Q 2.  Assertion : In moving from centre of a solid sphere to its surface, gravitational potential increases. 
Reason : Gravitational field strength increases. 
Q 3.  Assertion : There are two identical spherical bodies fixed in two positions as shown. While 
moving from A to B gravitational potential first increases then decreases. 
 
  Reason : At centre of A and B field strength will be zero. 
Q 4.  Assertion : If we plot potential versus x-coordinate graph along the x-axis, then field strength is 
zero where slope of V-x graph is zero. 
  Reason : If potential is function of x-only then 
     
dV
E
dx
?? 
Q 5.  Assertion : A particle is projected upwards with speed v and it goes to a height h. If we double the 
speed then it will move to height 4h. 
  Reason : In case of earth, acceleration due to gravity g varies as 
2
1
g
r
? (for r ? R) 
Q 6.  Assertion : In planetary motion angular momentum of system remains constant. But linear 
momentum does not remain constant. 
  Reason : Net torque on this system about any point is zero. 
Q 7.  Assertion : Plane of space satellite is always equitorial plane.  
  Reason : On the equator value of g is minimum. 
Q 8.  Assertion : On satellites we feel weightlessness. Moon is also a satellite of earth. But we do not 
feel weightlessness on moon. 
  Reason : Mass of moon is considerable. 
Q 9.  Assertion : Plane of geostationary satellites always passes through equator.  
  Reason : Geostationary satellites always lies above Moscow. 
Q 10.  Assertion : It we double the circular radius of a satellite, then its potential energy, kinetic energy 
and total mechanical energy will become half. 
Page 2


For JEE Advanced 
  Assertion and Reason  
Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : When two masses come closer, their gravitational potential energy decreases.  
  Reason : Two masses attract each other. 
Q 2.  Assertion : In moving from centre of a solid sphere to its surface, gravitational potential increases. 
Reason : Gravitational field strength increases. 
Q 3.  Assertion : There are two identical spherical bodies fixed in two positions as shown. While 
moving from A to B gravitational potential first increases then decreases. 
 
  Reason : At centre of A and B field strength will be zero. 
Q 4.  Assertion : If we plot potential versus x-coordinate graph along the x-axis, then field strength is 
zero where slope of V-x graph is zero. 
  Reason : If potential is function of x-only then 
     
dV
E
dx
?? 
Q 5.  Assertion : A particle is projected upwards with speed v and it goes to a height h. If we double the 
speed then it will move to height 4h. 
  Reason : In case of earth, acceleration due to gravity g varies as 
2
1
g
r
? (for r ? R) 
Q 6.  Assertion : In planetary motion angular momentum of system remains constant. But linear 
momentum does not remain constant. 
  Reason : Net torque on this system about any point is zero. 
Q 7.  Assertion : Plane of space satellite is always equitorial plane.  
  Reason : On the equator value of g is minimum. 
Q 8.  Assertion : On satellites we feel weightlessness. Moon is also a satellite of earth. But we do not 
feel weightlessness on moon. 
  Reason : Mass of moon is considerable. 
Q 9.  Assertion : Plane of geostationary satellites always passes through equator.  
  Reason : Geostationary satellites always lies above Moscow. 
Q 10.  Assertion : It we double the circular radius of a satellite, then its potential energy, kinetic energy 
and total mechanical energy will become half. 
  Reason : Orbital speed of a satellite.  
     
1
v
r
? 
  where r is its radius of orbit. 
Q 11.  Assertion : If the radius of earth is decreased keeping its mass constant, effective value of g may 
increase or decrease at pole. 
  Reason : Value of g on the surface of earth is given by 
2
GM
g
R
? . 
Answers 
1. (b) 2. (b) 3. (b) 4. (d) 5. (d) 6. (d) 7. (d) 8. (a) 9. (c) 10. (b) 11. (d) 
Solutions 
1.  As PE is proportional to negative of inverse of distance that is why PE decreases with decrease in 
separation. Thus assertion and reason are true but not the correct explanation. 
2.  Same explanation as Answer 1 
3.  While going from A to B, PE first increases, becomes maximum at middle and again decreases. 
Assertion and reason are true but not correct explanation. 
4.  at zero, slope of V - x graph E is zero if E is a function of x only, otherwise So, 
assertion is not always true. 
5.  and    
   
  ?  4hR + 4hh' = Rh' + hh'  
  ?  4hR = Rh' - 3hh' =(R- 3h)h' 
   
  So, assertion is false. 
6.  In planetary motion, angular momentum of the planet is constant but it is not true for the system. 
So, assertion is false. 
7.  Only geo-stationary satellites are on equatorial plane, not all. So, assertion is false. 
8.  Reason is true for explanation of assertion. 
9.  Assertion is true but reason is false (and even Moscow is not at equator). 
10.  Both assertion and reason are true but not correct explanation. 
   
Page 3


For JEE Advanced 
  Assertion and Reason  
Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : When two masses come closer, their gravitational potential energy decreases.  
  Reason : Two masses attract each other. 
Q 2.  Assertion : In moving from centre of a solid sphere to its surface, gravitational potential increases. 
Reason : Gravitational field strength increases. 
Q 3.  Assertion : There are two identical spherical bodies fixed in two positions as shown. While 
moving from A to B gravitational potential first increases then decreases. 
 
  Reason : At centre of A and B field strength will be zero. 
Q 4.  Assertion : If we plot potential versus x-coordinate graph along the x-axis, then field strength is 
zero where slope of V-x graph is zero. 
  Reason : If potential is function of x-only then 
     
dV
E
dx
?? 
Q 5.  Assertion : A particle is projected upwards with speed v and it goes to a height h. If we double the 
speed then it will move to height 4h. 
  Reason : In case of earth, acceleration due to gravity g varies as 
2
1
g
r
? (for r ? R) 
Q 6.  Assertion : In planetary motion angular momentum of system remains constant. But linear 
momentum does not remain constant. 
  Reason : Net torque on this system about any point is zero. 
Q 7.  Assertion : Plane of space satellite is always equitorial plane.  
  Reason : On the equator value of g is minimum. 
Q 8.  Assertion : On satellites we feel weightlessness. Moon is also a satellite of earth. But we do not 
feel weightlessness on moon. 
  Reason : Mass of moon is considerable. 
Q 9.  Assertion : Plane of geostationary satellites always passes through equator.  
  Reason : Geostationary satellites always lies above Moscow. 
Q 10.  Assertion : It we double the circular radius of a satellite, then its potential energy, kinetic energy 
and total mechanical energy will become half. 
  Reason : Orbital speed of a satellite.  
     
1
v
r
? 
  where r is its radius of orbit. 
Q 11.  Assertion : If the radius of earth is decreased keeping its mass constant, effective value of g may 
increase or decrease at pole. 
  Reason : Value of g on the surface of earth is given by 
2
GM
g
R
? . 
Answers 
1. (b) 2. (b) 3. (b) 4. (d) 5. (d) 6. (d) 7. (d) 8. (a) 9. (c) 10. (b) 11. (d) 
Solutions 
1.  As PE is proportional to negative of inverse of distance that is why PE decreases with decrease in 
separation. Thus assertion and reason are true but not the correct explanation. 
2.  Same explanation as Answer 1 
3.  While going from A to B, PE first increases, becomes maximum at middle and again decreases. 
Assertion and reason are true but not correct explanation. 
4.  at zero, slope of V - x graph E is zero if E is a function of x only, otherwise So, 
assertion is not always true. 
5.  and    
   
  ?  4hR + 4hh' = Rh' + hh'  
  ?  4hR = Rh' - 3hh' =(R- 3h)h' 
   
  So, assertion is false. 
6.  In planetary motion, angular momentum of the planet is constant but it is not true for the system. 
So, assertion is false. 
7.  Only geo-stationary satellites are on equatorial plane, not all. So, assertion is false. 
8.  Reason is true for explanation of assertion. 
9.  Assertion is true but reason is false (and even Moscow is not at equator). 
10.  Both assertion and reason are true but not correct explanation. 
   
11.  so as R is decreased, g increase, thus assertion is false. 
 
  Objective Questions Single Correct Option 
Q 1.  An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the 
earth. Suddenly due to internal explosion the satellite breaks into two parts of equal pieces. One 
part of the satellite stops just after the explosion. The increase in the mechanical energy of the 
system due to explosion will be (Given : acceleration due to gravity on the surface of earth is g) 
 (a) mgR  (b) 
mgR
2
   (c) 
mgR
4
   (d) 
3mgR
4
 
Q 2.  Gravitational field at the centre of a semicircle formed by a thin wire AB of mass
 
M and length l is
 
 (a) 
2
GM
l
along x-axis (b) 
2
GM
l ?
along y-axis (c) 
2
2 GM
l
?
along x-axis (d) 
2
2 GM
l
?
along y-axis 
Q 3.  A mass m is at a distance a from one end of a uniform rod of length l and mass M. The 
 gravitational force on the mass due to the rod is 
 
 (a) 
2
GMm
(a l) ?
   (b) 
GmM
a(l a) ?
   (c) 
2
GMm
a
   (d) 
2
GmM
2(l a) ?
 
Q 4.  A uniform ring of mass m is lying at a distance 3a from the centre of a sphere of mass M just 
over the sphere (where a is the radius of the ring as well as that of the sphere).
 
Then magnitude of 
gravitational force between them is 
 
 (a) 
2
GMm
8a
   (b) 
2
GMm
3a
   (c) 
2
GMm
3
a
   (d) 
2
GMm
3
8a
 
Q 5.  Four particles, each of mass M, move along a circle of radius R under the action of their mutual 
gravitational attraction. The speed of each particle is 
 (a) 
GM
R
   (b) 
GM
22
R
  (c) 
GM
(2 2 1)
R
?  (d) 
GM 2 2 1
R4
?
 
Page 4


For JEE Advanced 
  Assertion and Reason  
Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : When two masses come closer, their gravitational potential energy decreases.  
  Reason : Two masses attract each other. 
Q 2.  Assertion : In moving from centre of a solid sphere to its surface, gravitational potential increases. 
Reason : Gravitational field strength increases. 
Q 3.  Assertion : There are two identical spherical bodies fixed in two positions as shown. While 
moving from A to B gravitational potential first increases then decreases. 
 
  Reason : At centre of A and B field strength will be zero. 
Q 4.  Assertion : If we plot potential versus x-coordinate graph along the x-axis, then field strength is 
zero where slope of V-x graph is zero. 
  Reason : If potential is function of x-only then 
     
dV
E
dx
?? 
Q 5.  Assertion : A particle is projected upwards with speed v and it goes to a height h. If we double the 
speed then it will move to height 4h. 
  Reason : In case of earth, acceleration due to gravity g varies as 
2
1
g
r
? (for r ? R) 
Q 6.  Assertion : In planetary motion angular momentum of system remains constant. But linear 
momentum does not remain constant. 
  Reason : Net torque on this system about any point is zero. 
Q 7.  Assertion : Plane of space satellite is always equitorial plane.  
  Reason : On the equator value of g is minimum. 
Q 8.  Assertion : On satellites we feel weightlessness. Moon is also a satellite of earth. But we do not 
feel weightlessness on moon. 
  Reason : Mass of moon is considerable. 
Q 9.  Assertion : Plane of geostationary satellites always passes through equator.  
  Reason : Geostationary satellites always lies above Moscow. 
Q 10.  Assertion : It we double the circular radius of a satellite, then its potential energy, kinetic energy 
and total mechanical energy will become half. 
  Reason : Orbital speed of a satellite.  
     
1
v
r
? 
  where r is its radius of orbit. 
Q 11.  Assertion : If the radius of earth is decreased keeping its mass constant, effective value of g may 
increase or decrease at pole. 
  Reason : Value of g on the surface of earth is given by 
2
GM
g
R
? . 
Answers 
1. (b) 2. (b) 3. (b) 4. (d) 5. (d) 6. (d) 7. (d) 8. (a) 9. (c) 10. (b) 11. (d) 
Solutions 
1.  As PE is proportional to negative of inverse of distance that is why PE decreases with decrease in 
separation. Thus assertion and reason are true but not the correct explanation. 
2.  Same explanation as Answer 1 
3.  While going from A to B, PE first increases, becomes maximum at middle and again decreases. 
Assertion and reason are true but not correct explanation. 
4.  at zero, slope of V - x graph E is zero if E is a function of x only, otherwise So, 
assertion is not always true. 
5.  and    
   
  ?  4hR + 4hh' = Rh' + hh'  
  ?  4hR = Rh' - 3hh' =(R- 3h)h' 
   
  So, assertion is false. 
6.  In planetary motion, angular momentum of the planet is constant but it is not true for the system. 
So, assertion is false. 
7.  Only geo-stationary satellites are on equatorial plane, not all. So, assertion is false. 
8.  Reason is true for explanation of assertion. 
9.  Assertion is true but reason is false (and even Moscow is not at equator). 
10.  Both assertion and reason are true but not correct explanation. 
   
11.  so as R is decreased, g increase, thus assertion is false. 
 
  Objective Questions Single Correct Option 
Q 1.  An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the 
earth. Suddenly due to internal explosion the satellite breaks into two parts of equal pieces. One 
part of the satellite stops just after the explosion. The increase in the mechanical energy of the 
system due to explosion will be (Given : acceleration due to gravity on the surface of earth is g) 
 (a) mgR  (b) 
mgR
2
   (c) 
mgR
4
   (d) 
3mgR
4
 
Q 2.  Gravitational field at the centre of a semicircle formed by a thin wire AB of mass
 
M and length l is
 
 (a) 
2
GM
l
along x-axis (b) 
2
GM
l ?
along y-axis (c) 
2
2 GM
l
?
along x-axis (d) 
2
2 GM
l
?
along y-axis 
Q 3.  A mass m is at a distance a from one end of a uniform rod of length l and mass M. The 
 gravitational force on the mass due to the rod is 
 
 (a) 
2
GMm
(a l) ?
   (b) 
GmM
a(l a) ?
   (c) 
2
GMm
a
   (d) 
2
GmM
2(l a) ?
 
Q 4.  A uniform ring of mass m is lying at a distance 3a from the centre of a sphere of mass M just 
over the sphere (where a is the radius of the ring as well as that of the sphere).
 
Then magnitude of 
gravitational force between them is 
 
 (a) 
2
GMm
8a
   (b) 
2
GMm
3a
   (c) 
2
GMm
3
a
   (d) 
2
GMm
3
8a
 
Q 5.  Four particles, each of mass M, move along a circle of radius R under the action of their mutual 
gravitational attraction. The speed of each particle is 
 (a) 
GM
R
   (b) 
GM
22
R
  (c) 
GM
(2 2 1)
R
?  (d) 
GM 2 2 1
R4
?
 
Q 6.  A projectile is fired from the surface of earth of radius R with a velocity kve (where ve is the 
escape velocity from surface of earth and k < 1). Neglecting air resistance, the maximum height of 
rise from the centre of earth is 
 (a) 
2
R
k1 ?
   (b) k
2
R   (c) 
2
R
1k ?
   (d) kR 
Q 7.  Suppose a vertical tunnel is along the diameter of earth, assumed to be a sphere of uniform mass 
density ?. If a body of mass m is thrown in this tunnel, its acceleration at
 
a distance y from the 
centre is given by 
 
 (a) 
4
G ym
3
?
?  (b) 
3
y
4
??   (c) 
4
y
3
??   (d) 
4
Gy
3
?? 
Q 8.  A train of mass m moves with a velocity v on the equator from east to west. If ? is the angular 
speed of earth
 
about its axis and R is the radius of the earth then the normal reaction acting on the 
train is 
 (a) 
2
( R 2v) v
mg 1
g Rg
?? ? ? ?
??
??
??
  (b) 
2
( R v) v
mg 1 2
g Rg
?? ? ? ?
??
??
??
 
  (c) 
2
( R 2v) v
mg 1
g Rg
?? ? ? ?
??
??
??
  (d) 
2
( R v) v
mg 1 2
g Rg
?? ? ? ?
??
??
??
 
Q 9.  The figure represents a solid uniform sphere of mass M and radius R. A spherical cavity of radius 
r is at a distance a from the centre of the sphere. The gravitational field inside the cavity is 
 
  (a) non-uniform    (b) towards the centre of the cavity 
  (c) directly proportional to a   (d) All of the above 
Q 10.  If v e is the escape velocity for earth when a projectile is fired from the surface of earth. Then the 
escape velocity if the same projectile is fired from its centre is 
 (a) 
e
3
v
2
   (b) 
e
3
v
2
   (c) 
e
2
v
3
   (d) 
e
2
v
3
 
Q 11.  If the gravitational field intensity at a point is given by 
2.5
GM
g
r
? .
 
Then the potential at distance r is 
 (a) 
1.5
2GM
3r
?
   (b) 
3.5
GM
r
?
   (c) 
1.5
2GM
3r
   (d) 
3.5
GM
3r
 
Q 12.  Three identical particles each of mass M move along a common circular path of radius R under the 
mutual interaction of each other. The velocity of each particle is 
Page 5


For JEE Advanced 
  Assertion and Reason  
Directions : Choose the correct option. 
(a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion. 
(b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion. 
(c) If Assertion is true, but the Reason is false. 
(d) If Assertion is false but the Reason is true. 
Q 1.  Assertion : When two masses come closer, their gravitational potential energy decreases.  
  Reason : Two masses attract each other. 
Q 2.  Assertion : In moving from centre of a solid sphere to its surface, gravitational potential increases. 
Reason : Gravitational field strength increases. 
Q 3.  Assertion : There are two identical spherical bodies fixed in two positions as shown. While 
moving from A to B gravitational potential first increases then decreases. 
 
  Reason : At centre of A and B field strength will be zero. 
Q 4.  Assertion : If we plot potential versus x-coordinate graph along the x-axis, then field strength is 
zero where slope of V-x graph is zero. 
  Reason : If potential is function of x-only then 
     
dV
E
dx
?? 
Q 5.  Assertion : A particle is projected upwards with speed v and it goes to a height h. If we double the 
speed then it will move to height 4h. 
  Reason : In case of earth, acceleration due to gravity g varies as 
2
1
g
r
? (for r ? R) 
Q 6.  Assertion : In planetary motion angular momentum of system remains constant. But linear 
momentum does not remain constant. 
  Reason : Net torque on this system about any point is zero. 
Q 7.  Assertion : Plane of space satellite is always equitorial plane.  
  Reason : On the equator value of g is minimum. 
Q 8.  Assertion : On satellites we feel weightlessness. Moon is also a satellite of earth. But we do not 
feel weightlessness on moon. 
  Reason : Mass of moon is considerable. 
Q 9.  Assertion : Plane of geostationary satellites always passes through equator.  
  Reason : Geostationary satellites always lies above Moscow. 
Q 10.  Assertion : It we double the circular radius of a satellite, then its potential energy, kinetic energy 
and total mechanical energy will become half. 
  Reason : Orbital speed of a satellite.  
     
1
v
r
? 
  where r is its radius of orbit. 
Q 11.  Assertion : If the radius of earth is decreased keeping its mass constant, effective value of g may 
increase or decrease at pole. 
  Reason : Value of g on the surface of earth is given by 
2
GM
g
R
? . 
Answers 
1. (b) 2. (b) 3. (b) 4. (d) 5. (d) 6. (d) 7. (d) 8. (a) 9. (c) 10. (b) 11. (d) 
Solutions 
1.  As PE is proportional to negative of inverse of distance that is why PE decreases with decrease in 
separation. Thus assertion and reason are true but not the correct explanation. 
2.  Same explanation as Answer 1 
3.  While going from A to B, PE first increases, becomes maximum at middle and again decreases. 
Assertion and reason are true but not correct explanation. 
4.  at zero, slope of V - x graph E is zero if E is a function of x only, otherwise So, 
assertion is not always true. 
5.  and    
   
  ?  4hR + 4hh' = Rh' + hh'  
  ?  4hR = Rh' - 3hh' =(R- 3h)h' 
   
  So, assertion is false. 
6.  In planetary motion, angular momentum of the planet is constant but it is not true for the system. 
So, assertion is false. 
7.  Only geo-stationary satellites are on equatorial plane, not all. So, assertion is false. 
8.  Reason is true for explanation of assertion. 
9.  Assertion is true but reason is false (and even Moscow is not at equator). 
10.  Both assertion and reason are true but not correct explanation. 
   
11.  so as R is decreased, g increase, thus assertion is false. 
 
  Objective Questions Single Correct Option 
Q 1.  An artificial satellite of mass m is moving in a circular orbit at a height equal to the radius R of the 
earth. Suddenly due to internal explosion the satellite breaks into two parts of equal pieces. One 
part of the satellite stops just after the explosion. The increase in the mechanical energy of the 
system due to explosion will be (Given : acceleration due to gravity on the surface of earth is g) 
 (a) mgR  (b) 
mgR
2
   (c) 
mgR
4
   (d) 
3mgR
4
 
Q 2.  Gravitational field at the centre of a semicircle formed by a thin wire AB of mass
 
M and length l is
 
 (a) 
2
GM
l
along x-axis (b) 
2
GM
l ?
along y-axis (c) 
2
2 GM
l
?
along x-axis (d) 
2
2 GM
l
?
along y-axis 
Q 3.  A mass m is at a distance a from one end of a uniform rod of length l and mass M. The 
 gravitational force on the mass due to the rod is 
 
 (a) 
2
GMm
(a l) ?
   (b) 
GmM
a(l a) ?
   (c) 
2
GMm
a
   (d) 
2
GmM
2(l a) ?
 
Q 4.  A uniform ring of mass m is lying at a distance 3a from the centre of a sphere of mass M just 
over the sphere (where a is the radius of the ring as well as that of the sphere).
 
Then magnitude of 
gravitational force between them is 
 
 (a) 
2
GMm
8a
   (b) 
2
GMm
3a
   (c) 
2
GMm
3
a
   (d) 
2
GMm
3
8a
 
Q 5.  Four particles, each of mass M, move along a circle of radius R under the action of their mutual 
gravitational attraction. The speed of each particle is 
 (a) 
GM
R
   (b) 
GM
22
R
  (c) 
GM
(2 2 1)
R
?  (d) 
GM 2 2 1
R4
?
 
Q 6.  A projectile is fired from the surface of earth of radius R with a velocity kve (where ve is the 
escape velocity from surface of earth and k < 1). Neglecting air resistance, the maximum height of 
rise from the centre of earth is 
 (a) 
2
R
k1 ?
   (b) k
2
R   (c) 
2
R
1k ?
   (d) kR 
Q 7.  Suppose a vertical tunnel is along the diameter of earth, assumed to be a sphere of uniform mass 
density ?. If a body of mass m is thrown in this tunnel, its acceleration at
 
a distance y from the 
centre is given by 
 
 (a) 
4
G ym
3
?
?  (b) 
3
y
4
??   (c) 
4
y
3
??   (d) 
4
Gy
3
?? 
Q 8.  A train of mass m moves with a velocity v on the equator from east to west. If ? is the angular 
speed of earth
 
about its axis and R is the radius of the earth then the normal reaction acting on the 
train is 
 (a) 
2
( R 2v) v
mg 1
g Rg
?? ? ? ?
??
??
??
  (b) 
2
( R v) v
mg 1 2
g Rg
?? ? ? ?
??
??
??
 
  (c) 
2
( R 2v) v
mg 1
g Rg
?? ? ? ?
??
??
??
  (d) 
2
( R v) v
mg 1 2
g Rg
?? ? ? ?
??
??
??
 
Q 9.  The figure represents a solid uniform sphere of mass M and radius R. A spherical cavity of radius 
r is at a distance a from the centre of the sphere. The gravitational field inside the cavity is 
 
  (a) non-uniform    (b) towards the centre of the cavity 
  (c) directly proportional to a   (d) All of the above 
Q 10.  If v e is the escape velocity for earth when a projectile is fired from the surface of earth. Then the 
escape velocity if the same projectile is fired from its centre is 
 (a) 
e
3
v
2
   (b) 
e
3
v
2
   (c) 
e
2
v
3
   (d) 
e
2
v
3
 
Q 11.  If the gravitational field intensity at a point is given by 
2.5
GM
g
r
? .
 
Then the potential at distance r is 
 (a) 
1.5
2GM
3r
?
   (b) 
3.5
GM
r
?
   (c) 
1.5
2GM
3r
   (d) 
3.5
GM
3r
 
Q 12.  Three identical particles each of mass M move along a common circular path of radius R under the 
mutual interaction of each other. The velocity of each particle is 
 (a) 
GM 2
R3
   (b) 
GM
3R
   (c) 
GM
3R
   (d) 
2 GM
3R
 
Q 13.  If T be the period of revolution of a planet revolving around sun in an orbit of mean radius R, then 
identify the incorrect graph. 
  (a)  (b) (c)  (d) None of these 
Q 14.  A person brings a mass of 1 kg from infinity to a point A. Initially, the mass was at rest but it 
moves at a speed of 3 m/s as it reaches A. The work done by the person on the mass is - 5.5 J. The 
gravitational potential at A is 
  (a) - 1 J/kg   (b) - 4.5 J/kg   (c) - 5.5 J/kg   (d) - 10 J/kg 
Q 15.  With what minimum speed should m be projected from point C in presence of two fixed masses M 
each at A and B as shown in the figure such that mass m should
 
escape the gravitational attraction 
of A and 5? 
 
 (a) 
2GM
R
   (b) 
2 2GM
R
  (c) 
GM
2
R
   (d) 
GM
22
R
 
Q 16.  Consider two configurations of a system of three particles of masses m, 2m and 3m. The work 
 done by gravity in changing the
 
configuration of the system from figure (i) to figure (ii) is 
 
 (a) zero  (b) 
2
6Gm 1
1
a 2
??
?
??
??
 (c) 
2
6Gm 1
1
a 2
??
?
??
??
 (d) 
2
6Gm 1
2
a 2
??
?
??
??
 
Q 17.  A tunnel is dug along the diameter of the earth. There is a particle of mass m at the centre of the 
tunnel. Find the minimum velocity given to the particle so that is just reaches to the surface of the 
earth.(R = radius of earth) 
 (a) 
GM
R
   (b) 
GM
2R
   (c) 
2GM
R
 
  
(d) it will reach with the help of negligible velocity