DC Pandey Solutions: Gravitation - 2

# DC Pandey Solutions: Gravitation - 2 | Physics Class 11 - NEET PDF Download

``` Page 1

Introductory Exercise 10.3
Q 1.  The velocity of a particle is just equal to its escape velocity . Under such situation the
total mechanical energy of the particle is zero. Is this statement true or false?
Q 2.  What is the kinetic energy needed to project a body of mass m from the surface of
earth to infinity. Radius of earth is R and acceleration due to gravity on earth's surface
is g.
Q 3.  Two particles of masses 20 kg and 10 kg are initially at a distance of 1.0 m. Find the
speeds of the particles when the separation between them decreases to 0.5 m, if only
gravitational forces are acting.
Q 4.  A particle is fired vertically upward with a speed of 15 km/s. Find the speed of the
particle when it goes out of the earth's gravitational pull.
Q 5.  Show that if a body be projected vertically upward from the surface of the earth so as
to reach a height nR above the surface :
(i) the increase in its potential energy is
n
mgR
n1
??
??
?
??
,

(ii) the velocity with which it must be projected is
2ngR
n1 ?
,

where R is die radius of
the earth and m the mass of body.
Solutions
1.  Escape velocity is given to overcome the potential barrier and just free the particle
from a system, such that its total mechanical energy is just zero at infinity. So, the
statement is true.
2.
3.

Page 2

Introductory Exercise 10.3
Q 1.  The velocity of a particle is just equal to its escape velocity . Under such situation the
total mechanical energy of the particle is zero. Is this statement true or false?
Q 2.  What is the kinetic energy needed to project a body of mass m from the surface of
earth to infinity. Radius of earth is R and acceleration due to gravity on earth's surface
is g.
Q 3.  Two particles of masses 20 kg and 10 kg are initially at a distance of 1.0 m. Find the
speeds of the particles when the separation between them decreases to 0.5 m, if only
gravitational forces are acting.
Q 4.  A particle is fired vertically upward with a speed of 15 km/s. Find the speed of the
particle when it goes out of the earth's gravitational pull.
Q 5.  Show that if a body be projected vertically upward from the surface of the earth so as
to reach a height nR above the surface :
(i) the increase in its potential energy is
n
mgR
n1
??
??
?
??
,

(ii) the velocity with which it must be projected is
2ngR
n1 ?
,

where R is die radius of
the earth and m the mass of body.
Solutions
1.  Escape velocity is given to overcome the potential barrier and just free the particle
from a system, such that its total mechanical energy is just zero at infinity. So, the
statement is true.
2.
3.

= 1.63 × 10
-5
m/s

= 33 × 10
-5
m/s
4.

= 10 km/s
5.  (i)

(ii)

Introductory Exercise 10.4
Q 1.  If a body is released from a great distance from the centre of the earth, find its
velocity when it strikes the surface of the earth. Take R = 6400 km.
Q 2.  What quantities are constant in planetary motion?
Q 3.  Two satellites A and B of the same mass are orbiting the earth at altitudes R and 3R
respectively, where R is the radius of the earth. Taking their orbits to be circular
obtain the ratios of their kinetic and potential energies.
Q 4.  If a satellite is revolving close to a planet of density ?

with period T, show that the
quantity ?T
2

is a universal constant.
Q 5.  A satellite is revolving around a planet in a circular orbit. What will happen, if its
speed is increased from v0 to:
Page 3

Introductory Exercise 10.3
Q 1.  The velocity of a particle is just equal to its escape velocity . Under such situation the
total mechanical energy of the particle is zero. Is this statement true or false?
Q 2.  What is the kinetic energy needed to project a body of mass m from the surface of
earth to infinity. Radius of earth is R and acceleration due to gravity on earth's surface
is g.
Q 3.  Two particles of masses 20 kg and 10 kg are initially at a distance of 1.0 m. Find the
speeds of the particles when the separation between them decreases to 0.5 m, if only
gravitational forces are acting.
Q 4.  A particle is fired vertically upward with a speed of 15 km/s. Find the speed of the
particle when it goes out of the earth's gravitational pull.
Q 5.  Show that if a body be projected vertically upward from the surface of the earth so as
to reach a height nR above the surface :
(i) the increase in its potential energy is
n
mgR
n1
??
??
?
??
,

(ii) the velocity with which it must be projected is
2ngR
n1 ?
,

where R is die radius of
the earth and m the mass of body.
Solutions
1.  Escape velocity is given to overcome the potential barrier and just free the particle
from a system, such that its total mechanical energy is just zero at infinity. So, the
statement is true.
2.
3.

= 1.63 × 10
-5
m/s

= 33 × 10
-5
m/s
4.

= 10 km/s
5.  (i)

(ii)

Introductory Exercise 10.4
Q 1.  If a body is released from a great distance from the centre of the earth, find its
velocity when it strikes the surface of the earth. Take R = 6400 km.
Q 2.  What quantities are constant in planetary motion?
Q 3.  Two satellites A and B of the same mass are orbiting the earth at altitudes R and 3R
respectively, where R is the radius of the earth. Taking their orbits to be circular
obtain the ratios of their kinetic and potential energies.
Q 4.  If a satellite is revolving close to a planet of density ?

with period T, show that the
quantity ?T
2

is a universal constant.
Q 5.  A satellite is revolving around a planet in a circular orbit. What will happen, if its
speed is increased from v0 to:
(a)
0
1.5v    (b) 2v0
Solutions
1.  ?K = ?U

× 10
3
m/s = km/s = 11.2 km/s
2.  In planetary motion areal velocity, i.e., angular momentum and total mechanical
energy is conserved.
3.

4.

For = constant
5.

(a)
While,  so, the satellite will not escape from the planet, rather it
will revolve in elliptical orbit.
Page 4

Introductory Exercise 10.3
Q 1.  The velocity of a particle is just equal to its escape velocity . Under such situation the
total mechanical energy of the particle is zero. Is this statement true or false?
Q 2.  What is the kinetic energy needed to project a body of mass m from the surface of
earth to infinity. Radius of earth is R and acceleration due to gravity on earth's surface
is g.
Q 3.  Two particles of masses 20 kg and 10 kg are initially at a distance of 1.0 m. Find the
speeds of the particles when the separation between them decreases to 0.5 m, if only
gravitational forces are acting.
Q 4.  A particle is fired vertically upward with a speed of 15 km/s. Find the speed of the
particle when it goes out of the earth's gravitational pull.
Q 5.  Show that if a body be projected vertically upward from the surface of the earth so as
to reach a height nR above the surface :
(i) the increase in its potential energy is
n
mgR
n1
??
??
?
??
,

(ii) the velocity with which it must be projected is
2ngR
n1 ?
,

where R is die radius of
the earth and m the mass of body.
Solutions
1.  Escape velocity is given to overcome the potential barrier and just free the particle
from a system, such that its total mechanical energy is just zero at infinity. So, the
statement is true.
2.
3.

= 1.63 × 10
-5
m/s

= 33 × 10
-5
m/s
4.

= 10 km/s
5.  (i)

(ii)

Introductory Exercise 10.4
Q 1.  If a body is released from a great distance from the centre of the earth, find its
velocity when it strikes the surface of the earth. Take R = 6400 km.
Q 2.  What quantities are constant in planetary motion?
Q 3.  Two satellites A and B of the same mass are orbiting the earth at altitudes R and 3R
respectively, where R is the radius of the earth. Taking their orbits to be circular
obtain the ratios of their kinetic and potential energies.
Q 4.  If a satellite is revolving close to a planet of density ?

with period T, show that the
quantity ?T
2

is a universal constant.
Q 5.  A satellite is revolving around a planet in a circular orbit. What will happen, if its
speed is increased from v0 to:
(a)
0
1.5v    (b) 2v0
Solutions
1.  ?K = ?U

× 10
3
m/s = km/s = 11.2 km/s
2.  In planetary motion areal velocity, i.e., angular momentum and total mechanical
energy is conserved.
3.

4.

For = constant
5.

(a)
While,  so, the satellite will not escape from the planet, rather it
will revolve in elliptical orbit.
(b) As,  while, v =2vo i.e., the satellite will escape.

```

## Physics Class 11

102 videos|411 docs|121 tests

## FAQs on DC Pandey Solutions: Gravitation - 2 - Physics Class 11 - NEET

 1. What is the formula to calculate the gravitational force between two objects?
Ans. The formula to calculate the gravitational force between two objects is given by Newton's law of universal gravitation: F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.
 2. How does the gravitational force between two objects change if the distance between them is doubled?
Ans. According to Newton's law of universal gravitation, if the distance between two objects is doubled, the gravitational force between them decreases by a factor of four. This means that the force is inversely proportional to the square of the distance.
 3. What happens to the gravitational force if the mass of one object is doubled while keeping the other object's mass constant?
Ans. If the mass of one object is doubled while keeping the other object's mass constant, the gravitational force between them will also double. According to Newton's law of universal gravitation, the force is directly proportional to the product of the masses involved.
 4. Can the gravitational force between two objects ever be zero?
Ans. No, the gravitational force between two objects can never be zero as long as they have a non-zero mass. According to Newton's law of universal gravitation, the force is always present, no matter how small the masses or large the distance between them.
 5. How does the gravitational force vary with the mass of the objects involved?
Ans. The gravitational force between two objects varies directly with the masses of the objects. This means that if the mass of one or both objects increases, the gravitational force between them will also increase.

## Physics Class 11

102 videos|411 docs|121 tests

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