Tuesday, September 29, 2015

HC Verma solutions, Concepts of Physics, Part 1,Chapter 5, "Newton's Laws of Motion", QUESTIONS FOR SHORT ANSWER

QUESTIONS FOR SHORT ANSWER

1. The apparent weight of an object increases in an elevator while accelerating upward. A moongfaliwala sells his moongfali using a beam balance in an elevator. Will he gain more if the elevator is accelerating up?

  

Answer: A beam balance compares the weight of an object put at one side with respect to the standard weight put at the other side. So while the elevator is going up, weights on both sides of the balance will gain equally. The moongfaliwala thus would not gain more.     




2. A boy puts a heavy box of mass M on his head and jumps down from the top of a multi-storied building to the ground. How much is the force exerted by the box on his head during his free fall? Does the force greatly increase during the period he balances himself after striking the ground? 


Answer: During his free fall the box does not exert any force on the head of the boy. It can be explained by taking the frame of reference in the boy. Since the boy is accelerating downward with "g" acceleration, this frame will be a non-inertial frame. To apply Newton's law in a non-inertial frame we add a pseudo force(-ma) to the system along with the other forces acting on it, where a is the acceleration of the frame. In this case a=g. Consider the box as a system. The forces on it are gravity force weight of the box Mg downward, and the pseudo force upward (-Mg). Adding these forces we get zero. So no force is applied by the box on the boy.

           Now consider the period when he balances himself after striking the ground. The feet of the boy has come to rest and he tries to bring the box (that has gained velocity) to rest by pushing it up. So he applies a great force upward to decelerate it. And according to Newton's third law of motion, the box also applies equal and opposite force on the boy.




3. A person drops a coin. Describe the path of the coin as seen by the person if he is in (a) a car moving at a constant velocity and (b) in a free-falling elevator.


Answer: (a) A car moving with a constant velocity is an inertial frame of reference. So the person will see the dropped coin falling to the floor in a straight line.

            (b) A free falling elevator is a non-inertial frame of reference because it is accelerating towards the ground with g. So along with the force on the coin, its weight 'mg', we shall add a pseudo force '-mg' to it, where m is the mass of the coin. It results in zero force or no force on the coin. So the person in the free-falling elevator will see no movement in the coin. It will remain stable to the point where he dropped it. 




4. Is it possible for a particle to describe a curved path if no force acts on it? Does your answer depend on the frame of reference chosen to view the particle? 


Answer: The answer actually depends upon the frame of reference chosen. If it is an inertial frame then with no force there will not be a curved path for the particle. But if the frame of reference chosen is non-inertial, a pseudo force -ma will have to be applied to the particle where m is mass of the particle and a is the acceleration of the non-inertial frame. It will give the particle a pseudo acceleration '-a' as viewed from this frame. If the particle was moving with a uniform velocity in a line with some angle to the direction of 'a' with no force in the inertial frame, the path of the particle will appear curved if viewed from the non-inertial frame with acceleration a.


     

5. You are riding a car. The driver suddenly applies the brakes and you are pushed forward. Who pushed you forward.


Answer: When riding a car our body also moves with the velocity of the car and it does not want to change its state of uniform velocity due to inertia, as Newton's first law says. When the driver suddenly applies brakes the lower part of our body in contact with the car's seat come to rest with the car (due to friction) while the upper part moves forward in inertia. So due to the inertia of our body, our body is pushed forward.




6. It is sometimes heard that the inertial frame of reference is only an ideal concept and no such inertial frame actually exists.


Answer: In an inertial frame, acceleration a of a particle is zero if and only if Net force F on the particle is zero. For example, a book kept on a table has a=0 and sum of all forces on the book is zero, so we call earth an inertial frame but if accurately measured the sum of all forces on the book would not be zero. It will be very close to zero, so for all practical purposes we take the earth as an inertial frame but it is an ideal concept and no such inertial frame exist. 




7. An object is placed far away from all the objects that can exert force on it. A frame of reference is constructed by taking the origin and axes fixed in this object. Will the frame be necessarily inertial?


Answer: Since the origin and the axes are fixed in the object, the frame of reference will always move with it. The acceleration of the object with reference to this frame will always be zero. Now the sum of forces on the object will also be zero because no other object can exert force on it. So in this frame of reference always a=0 for F=0. So it is an inertial frame.




8. Figure (5-Q1) shows a light spring balance connected to two blocks of mass 20 kg each. The graduations in the balance measure the tension in the spring. (a) what is the reading of the balance? (b) will the reading change if the balance is heavy, say 2.0 kg? (c) what will happen if the spring is light but the blocks are unequal masses?
The figure for Q. No. - 8

Answer: (a) The reading in the balance is 20 kg. 

(b) Yes, if the balance is heavy the reading will change because the tension in the string will change.

(c) When the blocks are of unequal masses, there will be a net force on the system and it will start to move if the pulleys are frictionless. The tension in the string will change and so will be the reading of the balance. 




9. The acceleration of a particle is zero as measured from an inertial frame of reference. Can we conclude that no force acts on the particle?

 

Answer: It can not be concluded that no force acts on the particle. We can only say that net force or the resultant of all forces acting on the particle is zero.




10. Suppose that you are running fast in a field when you suddenly find a snake in front of you. You stop quickly. Which force is responsible for your deceleration?


Answer: It is the force of friction in backward direction between our feet and the ground that decelerates.




11. If you jump barefooted on a hard surface, your legs get injured. But they are not injured if you jump on a soft surface like sand or pillow. Explain.


Answer: On a hard surface our downward velocity quickly comes to zero, means the rate of change of velocity that is acceleration (in the upward direction) is high. It is due to the stronger force exerted by the hard surface on our legs so they get injured. On the other hand, if we jump on the soft surfaces like sand or pillow it takes more time to achieve zero velocity as our legs plunge to a distance. So the rate of change of velocity ie deceleration is lower because the soft surface exert lesser force on our legs and they are not injured.




12. According to Newton's third law, each team pulls the opposite team with equal force in a tug of war. Why then one team wins and other team loses?


Answer: Newton's third law connects the forces exerted by two bodies on one another but these two forces act on two different bodies and they never appear together on one body when it is considered as a system. So these forces will not cancel each other. In a tug of war when we consider a team as a system, the forces acting on it will be pull in the rope, the weight of the team, Normal force by the floor and force of friction between floor and feet. The net of these forces for each team may not be equal that is why one team wins and the other team loses.   



13. A spy jumps from an airplane with his parachute. The spy accelerates downward for some time when the parachute opens. The acceleration is suddenly checked and the spy slowly falls on the ground. Explain the action of a parachute in checking the acceleration. 


Answer: When the spy jumps the forces acting on him is - 1. His weight in the downward direction and 2. resistance of the air in the upward direction. The magnitude of resistance of air depends upon the area of the object available perpendicular to the direction of motion and velocity of the object. Before opening the parachute, this area is due to his body which is very small, so the air resistance is also very small. So the net downward force is hardly reduced and the spy accelerates downwards. But as the parachute opens, air begins to fill in it and its area gradually increases. In this period air resistance starts to increase and net downward force begins to reduce but it is still not zero that is why for some time he accelerates. But as the parachute opens fully, due to the wide area of the parachute and high velocity, the air resistance in upward direction gets greater than the weight of the spy and not only the acceleration is checked the high velocity achieved begins to decrease (deceleration) due to net upward force. But as the velocity reduces so does the air resistance. And both the forces adjust to become equal and opposite at some slower velocity at which he falls on the ground.



14. Consider a book lying on a table. The weight of the book and the normal force by the table on the book are equal in magnitude and opposite in direction. Is it an example of Newton's third law?


Answer: Yes. 



15. Two blocks of unequal masses are tied by a spring. The blocks are pulled stretching the spring slightly and the system is released on a friction-less horizontal platform. Are the forces due to the spring on the two blocks equal and opposite? If yes, is it an example of Newton's third law?


Answer: The forces due to the spring on the two blocks are equal and opposite. Yes, it is an example of Newton's third law.




16. When a train starts, the head of a standing passenger seems to be pushed backward. Analyze the situation from the ground frame. Does it really go backward? Coming back to to the train frame, how do you explain the backward movement of the head on the basis of Newton's law?

 

Answer: From the ground frame the head of the passenger in the train will look static while his lower part of the body will be moving forward with the train. Because according to the first law of motion, the head does not want to change the state of rest due to inertia.  

             From the train's frame, the lower part of the passenger moves forward with the frame because it is in contact with the seat and it will look at rest. Since the accelerating frame of the train is a non-inertial frame, so to explain it by Newton's laws of motion a pseudo force opposite to the direction of movement equal to 'ma' will have to be applied on the passenger. The upper part of the passenger not with contact with the seat moves backward due to this pseudo force.




17. A plumb bob is hung from the ceiling of a train compartment. If the train moves with an acceleration 'a' along a straight horizontal track, the string supporting the bob makes an angle tan-1(a/g) with the normal to the ceiling. Suppose the train moves on an inclined straight track with uniform velocity. If the angle of incline is tan-1(a/g), the string still makes the same angle with the normal to the ceiling. Can a person sitting inside the compartment tell by looking at the plumb line whether the train is accelerated on a horizontal straight track or it is going on an incline? If yes, how? If no, suggest a method to do so.

Answer: Since in both of the cases the angle that string makes with normal to the ceiling is same, a person sitting inside the compartment can not tell by looking at the plumb line whether the train is accelerated on a horizontal track or it is going on an incline. 

         To determine this he should know the weight of the bob and measure the tension in the string with a spring balance. If the tension and the weight of the bob are the same then the train is going with uniform velocity on an incline. If the tension in the string is more than the weight of the bob, the train is moving on a horizontal track with an acceleration. 

           It can be explained as in the figure below:--
Comparison of both situations
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Links to the Chapters



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".

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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


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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 - "Vector related Problems"

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Click here for "OBJECTIVE-II"

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36 comments:

  1. UnknownJuly 14, 2018 at 12:26 PM

    Kindly revise question 14 and 15 again
    This is not 3 rd law

    ReplyDelete
  2. unknownAugust 7, 2018 at 4:29 PM

    In ques 8( short ques) I think tension will not change if spring balance becomes heavy becoz tension depends on the mass of block which are hanging

    ReplyDelete
    Replies
    1. K K MISHRAAugust 9, 2018 at 10:49 AM

      Literally the tension in the string will not change but the reading of the balance will change because it is hanging. As you may have noticed in the case of electric wires that whatever maximum tension be given to the wires they still sag to balance the weight of the wire. Even in this case if the balance is heavy the strings on both the sides will not remain in a straight line. So the reading of the balance will show only the horizontal component of the tension in the strings. I meant to say that the horizontal pull on the balance will change which is responsible for the reading of the balance.

      Delete
    2. unknownAugust 13, 2018 at 12:30 PM

      Thanku so much sir
      Ur explanation is awesome...

      Delete
  3. unknownAugust 7, 2018 at 4:36 PM

    In ques 14 (short ques) since mg and normal both are acting on same body thus this is not an example of third law

    ReplyDelete
    Replies
    1. K K MISHRAAugust 9, 2018 at 10:56 AM

      When you place a book on a table, the book pushes the table by its weight mg and the table pushes the book with equal and opposite normal force mg.

      Delete
  4. unknownAugust 9, 2018 at 11:34 AM

    Sir I think normal by book and normal by table is a pair of action reaction ,and weight of book on bench and the gravitational force by which book pulls the earth is another pair of action reaction

    ReplyDelete
    Replies
    1. K K MISHRAAugust 17, 2018 at 9:21 AM

      Not the weight of the book on the bench but the weight of the book: The force by which the earth pulls the book is its weight and equally the book pulls the earth towards it- these are action -reactions. Similarly Due to its weight the book kept on the table presses the table by the amount of its weight and equally the table presses the book upward. You can visualise it by keeping the book in your hand. The book applies a force equal to its weight on your hand and to keep it in its place you apply equal amount of force in the opposite direction. It is the action-reaction pair. Similarly the weight of the book and your weight combined are pressing the floor through your feet and the floor is applying equal amount of force on your feet but in opposite direction i.e. upward. All these are examples of Newton's third law.
      I think there is no confusion now.

      Delete
  5. unknownAugust 15, 2018 at 12:09 PM

    Sir plss reply to my other queries
    I really need ur help

    ReplyDelete
  6. AnshAugust 20, 2018 at 9:31 PM

    sir in
    Q14. Consider a book lying on a table. The weight of the book and the normal force by the table on the book are equal in magnitude and opposite in direction. Is it an example of Newton's third law ?

    i think ans should be NO as weight of book is the force applied by book ON EARTH
    I agree magnitude and direction of weight of book is same to the force by book on table
    but The weight of the book and the normal force by the table on the book are not action reaction pair

    ReplyDelete
    Replies
    1. K K MISHRAAugust 21, 2018 at 1:09 AM

      Of course they are. The weight of the book is a gravitational force by the earth on the book and equal amount of gravitational force is applied by the book on the earth. That is a set of action-reaction. But I am not taking here the gravitational force between the book and the table but due to its weight the book pushes the table and the table applies equal and opposite amount of force.
      suppose you are pressing a wall by your hand, the wall also equally presses your hand. You are using your muscular force to press the wall, similarly the book also uses its weight (gravitational pull by the earth) to press the table. Even when you stand on the floor your weight and the upward force by the floor on you are example of action-reaction.
      Though weight is a gravitational force by the earth on a body, due to its weight it can perform the action of pressing something and each action has equal and opposite reaction.
      So no confusion at all.

      Delete
  7. SanketApril 23, 2019 at 2:01 AM

    Sir in the question 6th to set the frame of reference we take the body in order and in the body we set the origin and then calculate net external force which is zero but if we specify the position of the frame in body then we would encounter a atom and further if another neighbouring atom is charged and our frame atom is also charged then what about electrostatic force which for only these both atom would not be zero so is this still a inertial frame ?? The answers are extremely useful thank u sir 🤗🤗

    ReplyDelete
    Replies
    1. K K MISHRAApril 24, 2019 at 10:55 PM

      Dear student, if only two atoms are charged in a body and there is electrostatic force between them, they will tend to move along the direction of force. The adjacent atoms in the body will prevent the movement by reaction forces. Thus sum of all forces on these two atoms will be zero.
      For an inertial frame its velocity is either zero or uniform.

      Delete
    2. UnknownNovember 3, 2019 at 7:16 PM

      Thank u so much sir for clarifying so many doubts of mine !!🙏🙏

      Delete
  8. garima singhNovember 2, 2019 at 10:40 PM

    thanks a lot sir !! your explanation is mindblowing.
    sir i wanted to know the forces acting on the beam balance in 1st q with directions .
    also,
    in 2nd question cant we solve it in this way (i was solving in this way) :
    mg-N = mg
    where N is the normal reaction between the head and the box
    N = mg - mg = 0
    and sir how block gained the velocity when mg got cancelled with the mg acting upwards(pseudo force)?

    again sir thanks a lot

    ReplyDelete
    Replies
    1. K K MISHRANovember 3, 2019 at 9:02 AM

      Dear student, In Q-1 the forces of apparent weight on each side will be downward and the normal (Sum of weights on both sides) at the base of the balance will be upward.
      Ok. The velocity is always relative to a frame. Block does not gain velocity wrt the boy because no resultant force. But wrt ground force mg acts on it and it accelerates.

      Delete
    2. UnknownNovember 3, 2019 at 7:16 PM

      Thank u so much sir for clarifying so many doubts of mine !!🙏🙏

      Reply

      Delete
  9. garima singhNovember 2, 2019 at 10:50 PM

    sir in Q 3 does it mean that if the person see the falling coin through a freely falling elevator it will appear that the coin is at rest ?

    ReplyDelete
    Replies
    1. K K MISHRANovember 3, 2019 at 9:12 AM

      Yes, the coin will appear to be at rest with respect to the person.

      Delete
  10. garima singhNovember 2, 2019 at 11:08 PM

    sir can u give an example of Q 4

    ReplyDelete
    Replies
    1. K K MISHRANovember 3, 2019 at 9:20 AM

      The path of a horizontally moving object with a uniform velocity seen from a fee falling elevator.

      Delete
  11. garima singhNovember 2, 2019 at 11:30 PM

    This comment has been removed by the author.

    ReplyDelete
  12. garima singhNovember 2, 2019 at 11:46 PM

    sir in Q 5 the line in which u have mentioned :
    "When the driver suddenly applies brakes the lower part of our body in contact with the car's seat come to rest with the car (due to friction)"
    i think instead of 'due to friction ' it should be "due to brakes"
    please correct me if wrong (i know i am wrong) .

    ReplyDelete
    Replies
    1. K K MISHRANovember 3, 2019 at 9:56 AM

      Dear student, the brakes also work on friction. What I mean in this line that the car comes to rest along with its seat due to brakes applied and due to friction between the seat and ourselves the lower part of our body comes to rest. I think it is clear now.

      Delete
    2. garima singhNovember 4, 2019 at 8:27 AM

      crystal clear ...thank u sir

      Delete
  13. garima singhNovember 3, 2019 at 12:52 AM

    sir in Q 7 what is the significance of the line that u have mentioned :
    "Since the origin and the axes are fixed in the object, the frame of reference will always move with it. The acceleration of the object with reference to this frame will always be zero."

    ReplyDelete
    Replies
    1. K K MISHRANovember 3, 2019 at 10:02 AM

      You need to know the acceleration of the frame to define it inertial or non-inertial.

      Delete
    2. garima singhNovember 4, 2019 at 9:59 AM

      sir then in case if the frame of reference is fixed inside a lift (the type of question that we usually encounter) then the acceleration of the lift with respect to the frame will always be zero as well . but we dont consider the lift as inertial.

      Delete
    3. K K MISHRANovember 5, 2019 at 6:42 AM

      We need to find the acceleration of the frame with respect to a frame that is not accelerated (inertial). As in the case of lift we see its acceleration with respect to earth which we assume as inertial. In Q-7, since the body is not acted upon by a resultant force and hence no acceleration with some distant reference point (assumed). We do not consider acceleration of the frame with respect to the body in which it fixed.

      Delete
  14. garima singhNovember 4, 2019 at 8:25 AM

    sir in Q 13 the line saying
    " And both the forces adjust to become equal and opposite at some slower velocity at which he falls on the ground."

    does "both the forces" means the gravitational pull and the air resistance ? and if they are becoming equal and opposite does it mean the air resistance is acting upward on the spy with magnitude equal to the product of his mass and acceleration due to gravity? and if yes does it mean that the spy is coming down with a constant velocity?

    ReplyDelete
  15. garima singhNovember 4, 2019 at 9:17 AM

    sir can u please elaborate the mechanism involved in the working of spring balance asked in Q 8 because i am having a hard time in understanding that how it is just 20 kg . isnt the spring balance getting stretched from both the sides ?

    ReplyDelete
    Replies
    1. K K MISHRANovember 5, 2019 at 7:01 AM

      Dear student, When you use a spring balance to measure a weight, it is always pulled along both sides. Normally when it is hanged on a nail and a weight W is hanged on its lower end, the nail also pulls up the balance by a force W. So this pull is upward and the weight force is downward. So no resultant force on the balance. In this position the reading is taken.
      In this problem, it is the same situation in the horizontal direction.

      Delete
  16. garima singhNovember 4, 2019 at 10:52 AM

    sir in Q 17 in first diagram how sec theta is greater than 1?

    ReplyDelete
    Replies
    1. K K MISHRANovember 5, 2019 at 7:10 AM

      Dear student, sec theta is always = or > 1.
      Since sec theta =hypotenuse/base. As it is clear from the diagram that here hypotenuse>base, hence sec theta is greater than 1.

      Delete
  17. Miss esotericNovember 7, 2019 at 9:08 AM

    Thank u so much sir for clarifying so many doubts .....your explanation is just wow .....would like to meet you in person someday

    ReplyDelete

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