Monday, October 16, 2023

H C Verma solutions, The Special Theory of Relativity, Chapter-47, Objective-I, Concepts of Physics, Part-II

OBJECTIVE-I


       1. The magnitude of linear momentum of a particle moving at a relativistic speed v is proportional to 
(a) v
(b) 1 -v²/c²
(c) √(1 -v²/c²)
(d) none of these.       

ANSWER: (d).    

EXPLANATION: The magnitude of linear momentum of a particle moving with a relativistic speed v is 
p =mₒv/√(1 -v²/c²). 

So p is proportional to v/√(1 -v²/c²). None of the first three options matches it. Hence option (d) is correct. 





       2. As the speed of a particle increases, its rest mass 
(a) increases
(b) decreases
(c) remains the same
(d) changes.      

ANSWER: (c). 

EXPLANATION: With the increase in speed of a particle, its relativistic mass increases but the rest mass remains unchanged. Hence option (c) is correct.  





       3. An experimenter measures the length of a rod. Initially, the experimenter and the rod are at rest with respect to the lab. Consider the following statements.  
(A) If the rod starts moving parallel to its length but the observer stays at rest, the measured length will be reduced.
(B) If the rod stays at rest but the observer starts moving parallel to the measured length of the rod, the length will be reduced. 

(a) A is true but B is false.
(b) B is true but A is false.
(c) Both A and B are true. 
(d) Both A and B are false.        

ANSWER: (c).  

EXPLANATION: Any of the frames may be chosen as at rest, it is the relativistic speed that matters. In statement B if we take the frame of the observer as at rest the rod will still be moving. In fact, the moving observer will experience himself at rest and see the rod moving. So both cases are similar. Option (c) is correct.  





       4. An experimenter measures the length of a rod. In the cases listed, all motions are with respect to the lab and parallel to the length of the rod. In which of the cases the measured length will be minimal? 
(a) The rod and the experimenter move with the same speed v in the same direction.
(b) The rod and the experimenter move with the same speed v in opposite directions. 
(c) The rod moves at speed v but the experimenter stays at rest.
(d) The rod stays at rest but the experimenter moves with the speed v.     

ANSWER: (b). 

EXPLANATION: The measured length will be minimal in the case in which the relativistic speed between the observer and the rod will be maximum. Out of the four cases, the case in option (b) will have the maximum relativistic speed because both are moving in opposite directions. So option (b) is correct. 





       5. If the speed of a particle moving at a relativistic speed is doubled, its linear momentum will 
(a) become double
(b) become more than double
(c) remain equal
(d) become less than double.    

ANSWER: (b).  

EXPLANATION: The linear momentum p of the particle is proportional to 
v/√(1 -v²/c²). 

Hence if v is doubled, the ratio of new linear momentum p' to p will be, 
{2v/√(1 -4v²/c²)}/{v/√(1 -v²/c²)} 
=2√(1 -v²/c²)/√(1-4v²/c²)  
=2√{(c² -v²)/(c² -4v²)} 

Since (c² -v²) > (c² -4v²), 
the ratio (c²-v²)/(c²-4v²) will be greater than 1 and also the factor √{(c²-v²)/(c²-4v²)} will be greater than 1. So the above ratio p'/p will be greater than 2. 
    So in this case, the linear momentum will become more than double. Option (b) is correct. 





       6. If a constant force acts on a particle, its acceleration will
(a) remain constant
(b) gradually decrease 
(c) gradually increase
(d) be undefined.     

ANSWER: (b). 

EXPLANATION: The acceleration is, 
                           a =F/m. 

With the constant force F acting on the particle, its speed will continue increasing, But this will also result in increasing the relativistic mass of the particle. Since the acceleration is inversely proportional to the relativistic mass, the acceleration in this case will gradually decrease. Option (b) is correct.  





       7. A charged particle is projected at a very high-speed perpendicular to a uniform magnetic field. The particle will 
(a) move along a circle
(b) move along a curve with an increasing radius of curvature
(c) move along a curve with a decreasing radius of curvature
(d) move along a straight line.     

ANSWER: (b). 

EXPLANATION: When the speed of a charged particle is normal, the particle moving perpendicular to a uniform magnetic field starts moving along a circular path because the speed of the particle remains unchanged but the magnetic field changes its direction perpendicular to both the directions of speed and the magnetic field. 
   In the given case, the particle is moving at a very high speed, hence its relativistic mass will be more than its rest mass. The force on the particle by the magnetic field is, 
mv²/r =qvB,  
→r =mv/qB. 

Since r is proportional to m, the radius of the circle will be increased. Option (b) is correct. 
--------------------------

 Buy Home Furnishing

Click here for all links → kktutor.blogspot.com 

===<<<O>>>===


My Channel on YouTube  →  SimplePhysics with KK


Links to the Chapters


CHAPTER 47- The Special Theory of Relativity





CHAPTER- 34- Magnetic Field

CHAPTER- 29- Electric Field and Potential











CHAPTER- 28- Heat Transfer

OBJECTIVE -I







EXERCISES - Q51 to Q55


CHAPTER- 27-Specific Heat Capacities of Gases

CHAPTER- 26-Laws of Thermodynamics


CHAPTER- 25-CALORIMETRY

Questions for Short Answer

OBJECTIVE-I

OBJECTIVE-II


EXERCISES - Q-11 to Q-18


CHAPTER- 24-Kinetic Theory of Gases







CHAPTER- 23 - Heat and Temperature






CHAPTER- 17 - Light Waves




CHAPTER- 14 - Fluid Mechanics




CHAPTER- 13 - Fluid Mechanics


CHAPTER- 12 - Simple Harmonic Motion









CHAPTER- 11 - Gravitation





CHAPTER- 10 - Rotational Mechanics






CHAPTER- 9 - Center of Mass, Linear Momentum, Collision


CHAPTER- 8 - Work and Energy

Click here for → Question for Short Answers

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → Exercises (1-10)

Click here for → Exercises (11-20)

Click here for → Exercises (21-30)

Click here for → Exercises (31-42)

Click here for → Exercise(43-54)

CHAPTER- 7 - Circular Motion

Click here for → Questions for Short Answer 

Click here for → OBJECTIVE-I

Click here for → OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → EXERCISES (11-20)

Click here for → EXERCISES (21-30)

CHAPTER- 6 - Friction

Click here for → Questions for Short Answer

Click here for → OBJECTIVE-I

Click here for → Friction - OBJECTIVE-II

Click here for → EXERCISES (1-10)

Click here for → Exercises (11-20)

Click here for → EXERCISES (21-31)

For more practice on problems on friction solve these- "New Questions on Friction".

---------------------------------------------------------------------------------

CHAPTER- 5 - Newton's Laws of Motion


Click here for → QUESTIONS FOR SHORT ANSWER

Click here for→Newton's Laws of Motion,Exercises(Q.No. 13 to 27)

-------------------------------------------------------------------------------

CHAPTER- 4 - The Forces

The Forces-

"Questions for short Answers"    


Click here for "The Forces" - OBJECTIVE-I


Click here for "The Forces" - OBJECTIVE-II


Click here for "The Forces" - Exercises


--------------------------------------------------------------------------------------------------------------

CHAPTER- 3 - Kinematics - Rest and Motion


Click here for "Questions for short Answers"


Click here for "OBJECTIVE-I"


Click here for EXERCISES (Question number 1 to 10)


Click here for EXERCISES (Question number 11 to 20)


Click here for EXERCISES (Question number 21 to 30)


Click here for EXERCISES (Question number 31 to 40)


Click here for EXERCISES (Question number 41 to 52)


CHAPTER- 2 - "Physics and Mathematics"

Click here for "Questions for Short Answers"


Click here for "OBJECTIVE-II"

Posted by at
Labels: , , ,

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)