Courses

Gravitation (Part - 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

DC Pandey (Questions & Solutions) of Physics: NEET

Created by: Ciel Knowledge

NEET : Gravitation (Part - 2) - Physics, Solution by DC Pandey NEET Notes | EduRev

``` 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.

```
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

210 docs

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;