Gravitation Practice Questions - DPP for JEE

 Page 1


1. (a) When closer to the sun, velocity of planet will be greater. So time
taken in covering a given area will be less.
2. (b) Acceleration due to gravity,
g ? r (if r < R
E
) and
(if r > R
E
)
3. (a)
Hence,  or 
or, r = (gR
2
 / ?
2
)
1/3
4. (c) The gravitational field due to the ring at a distance  is given by
Attractive force = 
5. (d)
6. (a) The force of attraction between sphere and shaded position 
Page 2


1. (a) When closer to the sun, velocity of planet will be greater. So time
taken in covering a given area will be less.
2. (b) Acceleration due to gravity,
g ? r (if r < R
E
) and
(if r > R
E
)
3. (a)
Hence,  or 
or, r = (gR
2
 / ?
2
)
1/3
4. (c) The gravitational field due to the ring at a distance  is given by
Attractive force = 
5. (d)
6. (a) The force of attraction between sphere and shaded position 
7. (d) also 
 
8. (b) We choose reference point, infinity, where total energy of the
system is zero.
So, initial energy of the system = 0
Final energy = 
From conservation of energy,
Page 3


1. (a) When closer to the sun, velocity of planet will be greater. So time
taken in covering a given area will be less.
2. (b) Acceleration due to gravity,
g ? r (if r < R
E
) and
(if r > R
E
)
3. (a)
Hence,  or 
or, r = (gR
2
 / ?
2
)
1/3
4. (c) The gravitational field due to the ring at a distance  is given by
Attractive force = 
5. (d)
6. (a) The force of attraction between sphere and shaded position 
7. (d) also 
 
8. (b) We choose reference point, infinity, where total energy of the
system is zero.
So, initial energy of the system = 0
Final energy = 
From conservation of energy,
Initial energy = Final energy
or ...(1)
By conservation of linear momentum
 or 
Putting value of v
2
 in equation (1), we get
Similarly 
9. (c) Let mass of smaller sphere (which has to be removed) is m
Mass of the left over part of the sphere
Page 4


1. (a) When closer to the sun, velocity of planet will be greater. So time
taken in covering a given area will be less.
2. (b) Acceleration due to gravity,
g ? r (if r < R
E
) and
(if r > R
E
)
3. (a)
Hence,  or 
or, r = (gR
2
 / ?
2
)
1/3
4. (c) The gravitational field due to the ring at a distance  is given by
Attractive force = 
5. (d)
6. (a) The force of attraction between sphere and shaded position 
7. (d) also 
 
8. (b) We choose reference point, infinity, where total energy of the
system is zero.
So, initial energy of the system = 0
Final energy = 
From conservation of energy,
Initial energy = Final energy
or ...(1)
By conservation of linear momentum
 or 
Putting value of v
2
 in equation (1), we get
Similarly 
9. (c) Let mass of smaller sphere (which has to be removed) is m
Mass of the left over part of the sphere
Therefore gravitational field due to the left over part of the sphere
10. (a) The gravitational potential at the centre of uniform spherical shell
is equal to the gravitational potential at the surface of shell i.e.,
, where a is radius of spherical shell
Now, if the shell shrinks then its radius decrease then density increases,
but mass is constant. so from above expression if a decreases, then
V increases.
11. (d) Both decreases but variation are different.
12. (c) Net force towards centre of earth = 
Normal force 
Thus pressing force 
 constant and independent of x.
Tangential force, F = ma = mg' cos ?
Page 5


1. (a) When closer to the sun, velocity of planet will be greater. So time
taken in covering a given area will be less.
2. (b) Acceleration due to gravity,
g ? r (if r < R
E
) and
(if r > R
E
)
3. (a)
Hence,  or 
or, r = (gR
2
 / ?
2
)
1/3
4. (c) The gravitational field due to the ring at a distance  is given by
Attractive force = 
5. (d)
6. (a) The force of attraction between sphere and shaded position 
7. (d) also 
 
8. (b) We choose reference point, infinity, where total energy of the
system is zero.
So, initial energy of the system = 0
Final energy = 
From conservation of energy,
Initial energy = Final energy
or ...(1)
By conservation of linear momentum
 or 
Putting value of v
2
 in equation (1), we get
Similarly 
9. (c) Let mass of smaller sphere (which has to be removed) is m
Mass of the left over part of the sphere
Therefore gravitational field due to the left over part of the sphere
10. (a) The gravitational potential at the centre of uniform spherical shell
is equal to the gravitational potential at the surface of shell i.e.,
, where a is radius of spherical shell
Now, if the shell shrinks then its radius decrease then density increases,
but mass is constant. so from above expression if a decreases, then
V increases.
11. (d) Both decreases but variation are different.
12. (c) Net force towards centre of earth = 
Normal force 
Thus pressing force 
 constant and independent of x.
Tangential force, F = ma = mg' cos ?
Curve is parabolic and at . Hence (c).
13. (d) Variation of g with altitude is,
variation of g with depth is,
Equating g
h
 and g
d
, we get d = 2h
14. (b)
The K.E. acquired by the body at the surface 
15. (a) The total momentum will be zero and hence velocity will be zero
just after collisiion. The pull of earth will make it fall down.
16. (b) or 
Kinetic energy = 
In case of satellites P.E = – 2 K.E
and T.E = P. E + K. E