DPP for NEET: Daily Practice Problems, Ch 18: Gravitation - 1

# DPP for NEET: Daily Practice Problems, Ch 18: Gravitation - 1 | Physics Class 11 PDF Download

``` Page 1

DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A mass M splits into two parts m and (M – m), which are
then separated by a certain distance. What ratio of (m / M)
maximises the gravitational force between the parts. ?
(a) 2/3 (b) 3/4
(c) 1/2 (d) 1/3
Q.2 What would be the angular speed of earth, so that bodies
lying on equator may experience weightlessness ?
(g = 10m/s
2
and radius of earth = 6400 km)
(a) 1.25 × 10
–3
–2
(c) 1.25 × 10
–4
–1
Q.3 The speed with which the earth have to rotate on its axis so
that a person on the equator would weigh (3/5) th as much
as present will be -
(Take the equatorial radius as 6400 km.)
(a) 3.28 × 10
–4
–4
(c) 3.28 × 10
–3
–3
Q.4 On a planet (whose size is the same as that of earth and
mass 4 times to the earth) the energy needed to lift a 2kg
mass vertically upwards through 2m distance on the planet
is (g = 10m/sec
2
on the surface of earth) -
(a) 16 J (b) 32 J (c) 160 J (d) 320 J
Q.5 Two bodies of  mass  10
2
kg and 10
3
kg are lying 1m apart.
The gravitational potential at the mid-point of the line
joining them is -
(a) 0 (b) –1.47 Joule/kg
(c) 1.47 Joule/kg (d) –147 × 10
–7
Joule /kg
Page 2

DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A mass M splits into two parts m and (M – m), which are
then separated by a certain distance. What ratio of (m / M)
maximises the gravitational force between the parts. ?
(a) 2/3 (b) 3/4
(c) 1/2 (d) 1/3
Q.2 What would be the angular speed of earth, so that bodies
lying on equator may experience weightlessness ?
(g = 10m/s
2
and radius of earth = 6400 km)
(a) 1.25 × 10
–3
–2
(c) 1.25 × 10
–4
–1
Q.3 The speed with which the earth have to rotate on its axis so
that a person on the equator would weigh (3/5) th as much
as present will be -
(Take the equatorial radius as 6400 km.)
(a) 3.28 × 10
–4
–4
(c) 3.28 × 10
–3
–3
Q.4 On a planet (whose size is the same as that of earth and
mass 4 times to the earth) the energy needed to lift a 2kg
mass vertically upwards through 2m distance on the planet
is (g = 10m/sec
2
on the surface of earth) -
(a) 16 J (b) 32 J (c) 160 J (d) 320 J
Q.5 Two bodies of  mass  10
2
kg and 10
3
kg are lying 1m apart.
The gravitational potential at the mid-point of the line
joining them is -
(a) 0 (b) –1.47 Joule/kg
(c) 1.47 Joule/kg (d) –147 × 10
–7
Joule /kg
2
DPP/ P 18
Q.6 If g is the acceleration due to gravity on the earth’s surface,
the gain in P .E. of an object of mass m raised from the surface
of the earth to a height of the radius R of the earth is -
(a) mgR (b) 2mgR (c)
1
2
mgR (d)
1
4
mgR
Q.7 Four particles, each of mass m, are placed at the corners
of square and moving along a circle of radius r under the
influence of mutual gravitational  attraction. The speed of
each particle will be -
(a)
Gm
(2 2 1)
r
+ (b)
Gm
r
(c)
Gm 2 21
r4
æö
+
ç÷
èø
(d)
2 2Gm
r
Q.8 Three particles of equal mass m are situated at the vertices
of an equilateral triangle of side l. What should be the
velocity of each particle, so that they move on a circular
path without changing l ?
(a)
GM
2l
(b)
GM
l
(c)
2GM
l
(d)
GM
3 l
Q.9 What will be the acceleration due to gravity on the surface
of the moon if its radius is 1/4 th the radius of the earth and
its mass is 1/80 th the mass of the earth ?
(a) g/6 (b) g/5 (c) g/7 (d) g/8
Q.10 If the value of  'g' at a height h above the surface of the earth
is the same as at a depth x below it, then (both x and h being
much smaller than the radius of the earth)
(a) x = h (b) x = 2h (c)
h
x
2
= (d) x = h
2
Q.11 At what height above the earth's surface the acceleration
due to gravity will be 1/9 th of its value at the earth’s
surface? Radius of earth is 6400 km.
(a) 12800  km (b) 1280  km
(c) 128000  km (d) 128  km
Q.12 If the radius of the earth were to shrink by one percent, its
mass remaining the same, the acceleration due to gravity
on the earth’s surface would -
(a) decrease (b) remain unchanged
(c) increase (d) None of these
Q.13 At what height above the earth’s surface does the force of
gravity decrease by 10% ? Assume radius of earth to be
6370  km.
(a) 350 km. (b) 250 km. (c) 150 km. (d) 300 km.
Q.14 A particle is suspended from a spring and it stretches the
spring by 1 cm on the surface of earth. The same particle
will stretches the same spring at a place 800 km above earth
surface by -
(a) 0.79 cm (b) 0.1 c m
Q.15The change in the value of acceleration of earth towards
sun, when the moon comes from the position of solar
eclipse to the position on the other side of earth in line
with sun is (Mass of moon = 7.36 × 10
22
kg,  the orbital
radius of moon 3.8 × 10
8
m.
(a) 6.73 × 10
–2
m/s
2
(b) 6.73 × 10
–3
m/s
2
(c) 6.73 × 10
–4
m/s
2
(d) 6.73 × 10
–5
m/s
2
Q.16 The radius of the earth is R
e
and the acceleration due to gravity
at its surface is g. The work required in raising a body of
mass m to a height h form the surface of the earth will be -
(a)
e
mgh
h
1
R
æö
-
ç÷
èø
(b)
2
e
mgh
h
1
R
æö
+
ç÷
èø
(c)
e
mgh
h
1
R
æö
+
ç÷
èø
(d)
e
mg
h
1
R
æö
+
ç÷
èø
Q.17The masses and the radius of the earth and the moon are
M
1
, M
2
and R
1
, R
2
respectively their centres are at distance
d apart. The minimum speed with which a particle of mass
m should be projected form a point midway between the
two centres so as to escape to infinity will be -
(a)
12
G
2 (M M)
d
+ (b)
12
G
(M M)
d
+
(c)
12
G
(M M)
2d
+ (d)
1
2
M G
2
dM
Q.18 With what velocity must a body be thrown upward form the
surface of the earth so that it reaches a height of 10  R
e
?
earth’s mass M
e
= 6 × 10
24
e
= 6.4 × 10
6
m and
G = 6.67 × 10
–11
N–m
2
/kg
2
.
(a) 10.7 × 10
4
m/s (b) 10.7 × 10
3
m/s
(c) 10.7 × 10
5
m/s (d) 1.07 × 10
4
m/s
Page 3

DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A mass M splits into two parts m and (M – m), which are
then separated by a certain distance. What ratio of (m / M)
maximises the gravitational force between the parts. ?
(a) 2/3 (b) 3/4
(c) 1/2 (d) 1/3
Q.2 What would be the angular speed of earth, so that bodies
lying on equator may experience weightlessness ?
(g = 10m/s
2
and radius of earth = 6400 km)
(a) 1.25 × 10
–3
–2
(c) 1.25 × 10
–4
–1
Q.3 The speed with which the earth have to rotate on its axis so
that a person on the equator would weigh (3/5) th as much
as present will be -
(Take the equatorial radius as 6400 km.)
(a) 3.28 × 10
–4
–4
(c) 3.28 × 10
–3
–3
Q.4 On a planet (whose size is the same as that of earth and
mass 4 times to the earth) the energy needed to lift a 2kg
mass vertically upwards through 2m distance on the planet
is (g = 10m/sec
2
on the surface of earth) -
(a) 16 J (b) 32 J (c) 160 J (d) 320 J
Q.5 Two bodies of  mass  10
2
kg and 10
3
kg are lying 1m apart.
The gravitational potential at the mid-point of the line
joining them is -
(a) 0 (b) –1.47 Joule/kg
(c) 1.47 Joule/kg (d) –147 × 10
–7
Joule /kg
2
DPP/ P 18
Q.6 If g is the acceleration due to gravity on the earth’s surface,
the gain in P .E. of an object of mass m raised from the surface
of the earth to a height of the radius R of the earth is -
(a) mgR (b) 2mgR (c)
1
2
mgR (d)
1
4
mgR
Q.7 Four particles, each of mass m, are placed at the corners
of square and moving along a circle of radius r under the
influence of mutual gravitational  attraction. The speed of
each particle will be -
(a)
Gm
(2 2 1)
r
+ (b)
Gm
r
(c)
Gm 2 21
r4
æö
+
ç÷
èø
(d)
2 2Gm
r
Q.8 Three particles of equal mass m are situated at the vertices
of an equilateral triangle of side l. What should be the
velocity of each particle, so that they move on a circular
path without changing l ?
(a)
GM
2l
(b)
GM
l
(c)
2GM
l
(d)
GM
3 l
Q.9 What will be the acceleration due to gravity on the surface
of the moon if its radius is 1/4 th the radius of the earth and
its mass is 1/80 th the mass of the earth ?
(a) g/6 (b) g/5 (c) g/7 (d) g/8
Q.10 If the value of  'g' at a height h above the surface of the earth
is the same as at a depth x below it, then (both x and h being
much smaller than the radius of the earth)
(a) x = h (b) x = 2h (c)
h
x
2
= (d) x = h
2
Q.11 At what height above the earth's surface the acceleration
due to gravity will be 1/9 th of its value at the earth’s
surface? Radius of earth is 6400 km.
(a) 12800  km (b) 1280  km
(c) 128000  km (d) 128  km
Q.12 If the radius of the earth were to shrink by one percent, its
mass remaining the same, the acceleration due to gravity
on the earth’s surface would -
(a) decrease (b) remain unchanged
(c) increase (d) None of these
Q.13 At what height above the earth’s surface does the force of
gravity decrease by 10% ? Assume radius of earth to be
6370  km.
(a) 350 km. (b) 250 km. (c) 150 km. (d) 300 km.
Q.14 A particle is suspended from a spring and it stretches the
spring by 1 cm on the surface of earth. The same particle
will stretches the same spring at a place 800 km above earth
surface by -
(a) 0.79 cm (b) 0.1 c m
Q.15The change in the value of acceleration of earth towards
sun, when the moon comes from the position of solar
eclipse to the position on the other side of earth in line
with sun is (Mass of moon = 7.36 × 10
22
kg,  the orbital
radius of moon 3.8 × 10
8
m.
(a) 6.73 × 10
–2
m/s
2
(b) 6.73 × 10
–3
m/s
2
(c) 6.73 × 10
–4
m/s
2
(d) 6.73 × 10
–5
m/s
2
Q.16 The radius of the earth is R
e
and the acceleration due to gravity
at its surface is g. The work required in raising a body of
mass m to a height h form the surface of the earth will be -
(a)
e
mgh
h
1
R
æö
-
ç÷
èø
(b)
2
e
mgh
h
1
R
æö
+
ç÷
èø
(c)
e
mgh
h
1
R
æö
+
ç÷
èø
(d)
e
mg
h
1
R
æö
+
ç÷
èø
Q.17The masses and the radius of the earth and the moon are
M
1
, M
2
and R
1
, R
2
respectively their centres are at distance
d apart. The minimum speed with which a particle of mass
m should be projected form a point midway between the
two centres so as to escape to infinity will be -
(a)
12
G
2 (M M)
d
+ (b)
12
G
(M M)
d
+
(c)
12
G
(M M)
2d
+ (d)
1
2
M G
2
dM
Q.18 With what velocity must a body be thrown upward form the
surface of the earth so that it reaches a height of 10  R
e
?
earth’s mass M
e
= 6 × 10
24
e
= 6.4 × 10
6
m and
G = 6.67 × 10
–11
N–m
2
/kg
2
.
(a) 10.7 × 10
4
m/s (b) 10.7 × 10
3
m/s
(c) 10.7 × 10
5
m/s (d) 1.07 × 10
4
m/s
DPP/ P 18
3
Q.19 Two concentric shells of uniform density having masses M
1
and M
2
are situated as shown in the figure. The force on the
particle of mass m when it is located at r = b is
M
1
O
b
m
p
r
M
2
(a)
1
2
GMm
b
(b)
2
2
GMm
b
(c)
12
2
() M Mm
G
b
+
(d)
12
2
() M Mm
G
b
-
Q.20What is the mass of the planet that has a satellite whose
time period is T and orbital radius is r?
(a)
23
2
r
GT
4p
(b)
23
2
3p r
GT
(c)
23
3
r
GT
4p
(d)
2
2
T
GT
4p
DIRECTIONS (Q.21-Q.23) : In the following questions, more than
and mark it according to the following codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21 The gravitational force between two point masses m
1
and
m
2
at separation r is given by
12
2
mm
Fk
r
=
The constant k doesn't
(1) depend on medium between masses
(2) depend on the place
(3) depend on time
(4) depend on system of units
Q.22Which of the following statements about the gravitional
constant are false ?
(1) It is a force
(2) It has no unit
(3) It has same value in all system of units
(4) It doesn’t depend on the value of the masses
Q.23 Spot the correct statements :
The acceleration due to gravity ‘g’ decreases if
(1) We go down from the surface of the earth towards its
centre
(2) We go up from the surface of the earth
(3) The rotational velocity of the earth is increased
(4) We go from the equator towards the poles on the
surface of the earth
DIRECTIONS (Q.24-Q.26) : Read the passage given below and
answer the questions that follows :
The orbit of Pluto is much more eccentric than the orbits of the
other planets. That is, instead of being nearly circular, the orbit
is noticeably elliptical. The point in the orbit nearest to the sun
is called the perihelion and the point farthest from the sun is
called the aphelion.
Sun
Perihelion Aphelion
Q.24 At perihelion, the gravitational potential energy of Pluto
in its orbit has
(a) its maximum value
(b) its minimum value
(c) the same value as at every other point in the orbit
(d) value which depends on sense of rotation
Q.25 At perihelion, the mechanical energy of Pluto’s orbit has
(a) its maximum value
(b) its minimum value
(c) the same value as at every other point in the orbit
(d) value which depends on sense of rotation
Q.26As Pluto moves from the perihelion to the aphelion, the
work done by gravitational pull of Sun on Pluto is
(a) is zero
(b) is positive
(c) is negative
(d) depends on sense of rotation
Page 4

DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A mass M splits into two parts m and (M – m), which are
then separated by a certain distance. What ratio of (m / M)
maximises the gravitational force between the parts. ?
(a) 2/3 (b) 3/4
(c) 1/2 (d) 1/3
Q.2 What would be the angular speed of earth, so that bodies
lying on equator may experience weightlessness ?
(g = 10m/s
2
and radius of earth = 6400 km)
(a) 1.25 × 10
–3
–2
(c) 1.25 × 10
–4
–1
Q.3 The speed with which the earth have to rotate on its axis so
that a person on the equator would weigh (3/5) th as much
as present will be -
(Take the equatorial radius as 6400 km.)
(a) 3.28 × 10
–4
–4
(c) 3.28 × 10
–3
–3
Q.4 On a planet (whose size is the same as that of earth and
mass 4 times to the earth) the energy needed to lift a 2kg
mass vertically upwards through 2m distance on the planet
is (g = 10m/sec
2
on the surface of earth) -
(a) 16 J (b) 32 J (c) 160 J (d) 320 J
Q.5 Two bodies of  mass  10
2
kg and 10
3
kg are lying 1m apart.
The gravitational potential at the mid-point of the line
joining them is -
(a) 0 (b) –1.47 Joule/kg
(c) 1.47 Joule/kg (d) –147 × 10
–7
Joule /kg
2
DPP/ P 18
Q.6 If g is the acceleration due to gravity on the earth’s surface,
the gain in P .E. of an object of mass m raised from the surface
of the earth to a height of the radius R of the earth is -
(a) mgR (b) 2mgR (c)
1
2
mgR (d)
1
4
mgR
Q.7 Four particles, each of mass m, are placed at the corners
of square and moving along a circle of radius r under the
influence of mutual gravitational  attraction. The speed of
each particle will be -
(a)
Gm
(2 2 1)
r
+ (b)
Gm
r
(c)
Gm 2 21
r4
æö
+
ç÷
èø
(d)
2 2Gm
r
Q.8 Three particles of equal mass m are situated at the vertices
of an equilateral triangle of side l. What should be the
velocity of each particle, so that they move on a circular
path without changing l ?
(a)
GM
2l
(b)
GM
l
(c)
2GM
l
(d)
GM
3 l
Q.9 What will be the acceleration due to gravity on the surface
of the moon if its radius is 1/4 th the radius of the earth and
its mass is 1/80 th the mass of the earth ?
(a) g/6 (b) g/5 (c) g/7 (d) g/8
Q.10 If the value of  'g' at a height h above the surface of the earth
is the same as at a depth x below it, then (both x and h being
much smaller than the radius of the earth)
(a) x = h (b) x = 2h (c)
h
x
2
= (d) x = h
2
Q.11 At what height above the earth's surface the acceleration
due to gravity will be 1/9 th of its value at the earth’s
surface? Radius of earth is 6400 km.
(a) 12800  km (b) 1280  km
(c) 128000  km (d) 128  km
Q.12 If the radius of the earth were to shrink by one percent, its
mass remaining the same, the acceleration due to gravity
on the earth’s surface would -
(a) decrease (b) remain unchanged
(c) increase (d) None of these
Q.13 At what height above the earth’s surface does the force of
gravity decrease by 10% ? Assume radius of earth to be
6370  km.
(a) 350 km. (b) 250 km. (c) 150 km. (d) 300 km.
Q.14 A particle is suspended from a spring and it stretches the
spring by 1 cm on the surface of earth. The same particle
will stretches the same spring at a place 800 km above earth
surface by -
(a) 0.79 cm (b) 0.1 c m
Q.15The change in the value of acceleration of earth towards
sun, when the moon comes from the position of solar
eclipse to the position on the other side of earth in line
with sun is (Mass of moon = 7.36 × 10
22
kg,  the orbital
radius of moon 3.8 × 10
8
m.
(a) 6.73 × 10
–2
m/s
2
(b) 6.73 × 10
–3
m/s
2
(c) 6.73 × 10
–4
m/s
2
(d) 6.73 × 10
–5
m/s
2
Q.16 The radius of the earth is R
e
and the acceleration due to gravity
at its surface is g. The work required in raising a body of
mass m to a height h form the surface of the earth will be -
(a)
e
mgh
h
1
R
æö
-
ç÷
èø
(b)
2
e
mgh
h
1
R
æö
+
ç÷
èø
(c)
e
mgh
h
1
R
æö
+
ç÷
èø
(d)
e
mg
h
1
R
æö
+
ç÷
èø
Q.17The masses and the radius of the earth and the moon are
M
1
, M
2
and R
1
, R
2
respectively their centres are at distance
d apart. The minimum speed with which a particle of mass
m should be projected form a point midway between the
two centres so as to escape to infinity will be -
(a)
12
G
2 (M M)
d
+ (b)
12
G
(M M)
d
+
(c)
12
G
(M M)
2d
+ (d)
1
2
M G
2
dM
Q.18 With what velocity must a body be thrown upward form the
surface of the earth so that it reaches a height of 10  R
e
?
earth’s mass M
e
= 6 × 10
24
e
= 6.4 × 10
6
m and
G = 6.67 × 10
–11
N–m
2
/kg
2
.
(a) 10.7 × 10
4
m/s (b) 10.7 × 10
3
m/s
(c) 10.7 × 10
5
m/s (d) 1.07 × 10
4
m/s
DPP/ P 18
3
Q.19 Two concentric shells of uniform density having masses M
1
and M
2
are situated as shown in the figure. The force on the
particle of mass m when it is located at r = b is
M
1
O
b
m
p
r
M
2
(a)
1
2
GMm
b
(b)
2
2
GMm
b
(c)
12
2
() M Mm
G
b
+
(d)
12
2
() M Mm
G
b
-
Q.20What is the mass of the planet that has a satellite whose
time period is T and orbital radius is r?
(a)
23
2
r
GT
4p
(b)
23
2
3p r
GT
(c)
23
3
r
GT
4p
(d)
2
2
T
GT
4p
DIRECTIONS (Q.21-Q.23) : In the following questions, more than
and mark it according to the following codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21 The gravitational force between two point masses m
1
and
m
2
at separation r is given by
12
2
mm
Fk
r
=
The constant k doesn't
(1) depend on medium between masses
(2) depend on the place
(3) depend on time
(4) depend on system of units
Q.22Which of the following statements about the gravitional
constant are false ?
(1) It is a force
(2) It has no unit
(3) It has same value in all system of units
(4) It doesn’t depend on the value of the masses
Q.23 Spot the correct statements :
The acceleration due to gravity ‘g’ decreases if
(1) We go down from the surface of the earth towards its
centre
(2) We go up from the surface of the earth
(3) The rotational velocity of the earth is increased
(4) We go from the equator towards the poles on the
surface of the earth
DIRECTIONS (Q.24-Q.26) : Read the passage given below and
answer the questions that follows :
The orbit of Pluto is much more eccentric than the orbits of the
other planets. That is, instead of being nearly circular, the orbit
is noticeably elliptical. The point in the orbit nearest to the sun
is called the perihelion and the point farthest from the sun is
called the aphelion.
Sun
Perihelion Aphelion
Q.24 At perihelion, the gravitational potential energy of Pluto
in its orbit has
(a) its maximum value
(b) its minimum value
(c) the same value as at every other point in the orbit
(d) value which depends on sense of rotation
Q.25 At perihelion, the mechanical energy of Pluto’s orbit has
(a) its maximum value
(b) its minimum value
(c) the same value as at every other point in the orbit
(d) value which depends on sense of rotation
Q.26As Pluto moves from the perihelion to the aphelion, the
work done by gravitational pull of Sun on Pluto is
(a) is zero
(b) is positive
(c) is negative
(d) depends on sense of rotation
4
DPP/ P 18
DIRECTIONS (Q. 27-Q.29) : Each of these qu estions contains two
statements: S tatement-1 (Assertion) and S tatement-2 (Reason).
Each of these questions has four alternative choices, only one of
which is the correct answer . Y ou have to select the correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.
Q.27 Statement-1 : Gravitational force between two particles is
negligibly small compared to the electrical force.
Statement-2 :The electrical force is experienced by charged
particles only .
Q.28 Statement-1 :The universal gravitational constant is same
as acceleration due to gravity.
Statement-2 :Gravitional constant and acceleration due to
gravity have different dimensional formula.
Q.29 Statement-1 :There is no effect of rotation of earth on the
value of acceleration due to gravity at poles.
Statement-2 :Rotation of earth is about polar axis.
```

## Physics Class 11

118 videos|470 docs|189 tests

## Physics Class 11

118 videos|470 docs|189 tests

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