Gravitation Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. A Planet is revolving around the sun.
Which of the following is correct option?
(a) The time taken in travelling DAB is less than that for BCD
(b) The time taken in travelling DAB is  greater than that for BCD
(c) The time taken in travelling CDA is less than that for ABC
(d) The time taken in travelling CDA is greater than that for ABC
2. Which graph correctly presents the variation of acceleration due to
gravity with the distance from the centre of the earth (radius of the earth
=R
E
)?
Page 2


PART-I (Single Correct MCQs)
1. A Planet is revolving around the sun.
Which of the following is correct option?
(a) The time taken in travelling DAB is less than that for BCD
(b) The time taken in travelling DAB is  greater than that for BCD
(c) The time taken in travelling CDA is less than that for ABC
(d) The time taken in travelling CDA is greater than that for ABC
2. Which graph correctly presents the variation of acceleration due to
gravity with the distance from the centre of the earth (radius of the earth
=R
E
)?
(a)
(b)
(c)
(d)
3. The mean radius of earth is R, its angular speed on its own axis is ? and
the acceleration due to gravity at earth’s surface is g. What will be the
radius of the orbit of a geostationary satellite?
(a) (R
2
g / ?
2
)
1/3
(b) (Rg / ?
2
)
1/3
(c) (R
2
?
2
 / g)
1/3
Page 3


PART-I (Single Correct MCQs)
1. A Planet is revolving around the sun.
Which of the following is correct option?
(a) The time taken in travelling DAB is less than that for BCD
(b) The time taken in travelling DAB is  greater than that for BCD
(c) The time taken in travelling CDA is less than that for ABC
(d) The time taken in travelling CDA is greater than that for ABC
2. Which graph correctly presents the variation of acceleration due to
gravity with the distance from the centre of the earth (radius of the earth
=R
E
)?
(a)
(b)
(c)
(d)
3. The mean radius of earth is R, its angular speed on its own axis is ? and
the acceleration due to gravity at earth’s surface is g. What will be the
radius of the orbit of a geostationary satellite?
(a) (R
2
g / ?
2
)
1/3
(b) (Rg / ?
2
)
1/3
(c) (R
2
?
2
 / g)
1/3
(d) (R
2
g / ?)
1/3
4. A uniform ring of mass m and radius r is placed directly
above a uniform sphere of mass M and of equal radius. The
centre of the ring is directly above the centre of the sphere
at a distance  as shown in the figure.
The gravitational force exerted by the sphere on the ring will be
(a)
(b) (c) 
(d)
5. A satellite revolves around the earth of radius R in a circular orbit of
radius 3R. Then what is the percentage increase in energy required to
lift it to an orbit of radius 5R ?
(a) 10% (b) 20%
(c) 30%
(d) 40%
6. The gravitational force of attraction between a uniform sphere of mass
M and a uniform rod of length l and mass m oriented as shown is
(a)
(b)
(c) Mmr
2
 + l
(d) (r
2
 + l) mM
7. A satellite of mass m revolves around the earth of radius R at a height ‘x’
Page 4


PART-I (Single Correct MCQs)
1. A Planet is revolving around the sun.
Which of the following is correct option?
(a) The time taken in travelling DAB is less than that for BCD
(b) The time taken in travelling DAB is  greater than that for BCD
(c) The time taken in travelling CDA is less than that for ABC
(d) The time taken in travelling CDA is greater than that for ABC
2. Which graph correctly presents the variation of acceleration due to
gravity with the distance from the centre of the earth (radius of the earth
=R
E
)?
(a)
(b)
(c)
(d)
3. The mean radius of earth is R, its angular speed on its own axis is ? and
the acceleration due to gravity at earth’s surface is g. What will be the
radius of the orbit of a geostationary satellite?
(a) (R
2
g / ?
2
)
1/3
(b) (Rg / ?
2
)
1/3
(c) (R
2
?
2
 / g)
1/3
(d) (R
2
g / ?)
1/3
4. A uniform ring of mass m and radius r is placed directly
above a uniform sphere of mass M and of equal radius. The
centre of the ring is directly above the centre of the sphere
at a distance  as shown in the figure.
The gravitational force exerted by the sphere on the ring will be
(a)
(b) (c) 
(d)
5. A satellite revolves around the earth of radius R in a circular orbit of
radius 3R. Then what is the percentage increase in energy required to
lift it to an orbit of radius 5R ?
(a) 10% (b) 20%
(c) 30%
(d) 40%
6. The gravitational force of attraction between a uniform sphere of mass
M and a uniform rod of length l and mass m oriented as shown is
(a)
(b)
(c) Mmr
2
 + l
(d) (r
2
 + l) mM
7. A satellite of mass m revolves around the earth of radius R at a height ‘x’
from its surface. If g is the acceleration due to gravity on the surface of the
earth, the orbital speed of the satellite is
(a)
(b)
(c) gx (d)  
8. Two hypothetical planets of masses m
1
 and m
2
 are at rest when they are
infinite distance apart. Because of the gravitational force they move
towards each other along the line joining their centres.
What is their speed when their separation is ‘d’?
(Speed of m
1
 is v
1
 and that of m
2
 is v
2
)
(a) v
1
 = v
2
(b) , 
(c) , 
(d) , 
9. The gravitational field, due to the ‘left over part’ of a uniform sphere
(from which a part as shown, has been ‘removed out’), at a very far off
point, P, located as shown, would be (nearly):
Page 5


PART-I (Single Correct MCQs)
1. A Planet is revolving around the sun.
Which of the following is correct option?
(a) The time taken in travelling DAB is less than that for BCD
(b) The time taken in travelling DAB is  greater than that for BCD
(c) The time taken in travelling CDA is less than that for ABC
(d) The time taken in travelling CDA is greater than that for ABC
2. Which graph correctly presents the variation of acceleration due to
gravity with the distance from the centre of the earth (radius of the earth
=R
E
)?
(a)
(b)
(c)
(d)
3. The mean radius of earth is R, its angular speed on its own axis is ? and
the acceleration due to gravity at earth’s surface is g. What will be the
radius of the orbit of a geostationary satellite?
(a) (R
2
g / ?
2
)
1/3
(b) (Rg / ?
2
)
1/3
(c) (R
2
?
2
 / g)
1/3
(d) (R
2
g / ?)
1/3
4. A uniform ring of mass m and radius r is placed directly
above a uniform sphere of mass M and of equal radius. The
centre of the ring is directly above the centre of the sphere
at a distance  as shown in the figure.
The gravitational force exerted by the sphere on the ring will be
(a)
(b) (c) 
(d)
5. A satellite revolves around the earth of radius R in a circular orbit of
radius 3R. Then what is the percentage increase in energy required to
lift it to an orbit of radius 5R ?
(a) 10% (b) 20%
(c) 30%
(d) 40%
6. The gravitational force of attraction between a uniform sphere of mass
M and a uniform rod of length l and mass m oriented as shown is
(a)
(b)
(c) Mmr
2
 + l
(d) (r
2
 + l) mM
7. A satellite of mass m revolves around the earth of radius R at a height ‘x’
from its surface. If g is the acceleration due to gravity on the surface of the
earth, the orbital speed of the satellite is
(a)
(b)
(c) gx (d)  
8. Two hypothetical planets of masses m
1
 and m
2
 are at rest when they are
infinite distance apart. Because of the gravitational force they move
towards each other along the line joining their centres.
What is their speed when their separation is ‘d’?
(Speed of m
1
 is v
1
 and that of m
2
 is v
2
)
(a) v
1
 = v
2
(b) , 
(c) , 
(d) , 
9. The gravitational field, due to the ‘left over part’ of a uniform sphere
(from which a part as shown, has been ‘removed out’), at a very far off
point, P, located as shown, would be (nearly):
(a)
(b)
(c)
(d)
10. A uniform spherical shell gradually shrinks maintaining its shape. The
gravitational potential at the centre
(a) increases
(b) decreases
(c) remains constant
(d) cannot say
11. Consider Earth to be a homogeneous sphere. Scientist A goes deep
down in a mine and scientist B goes high up in a balloon. The
gravitational field measured by
(a) A goes on decreasing and that by B goes on increasing
(b) B goes on decreasing and that by A goes on increasing
(c) each decreases at the same rate
(d) each decreases at different rates
12. 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
acceleration of the particle varies with x (distance of the particle from the
centre) according to