DC Pandey Solutions: Gravitation - 2 | DC Pandey Solutions for NEET Physics 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.