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D Devendra Khairwa
The FBD of the loop is given below :                                                  Using equilibrium conditions we can write :                                                 and                                        Consider  OPQ, we have :                                                  or                                               Using l in above equation we get :                  ...

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D Devendra Khairwa
Frequency of rotation is :                                                 The required condition so that man will not fall :                                                or                                          or                                          or                                            And thus :                                                                    Thus the...

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D Devendra Khairwa
The motorcyclist does not drop down when he is at the uppermost point because of their weight and the normal force is balanced by the centripetal force.                                                  or                                              At minimum velocity, the normal reaction is zero. So the equation becomes :                                                              or       ...

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D Devendra Khairwa
Frequency of revolution is :                                                    (i) Case 1 :- When coin is placed at 4 cm :                                            Radius  =  0.04 m                                     Angular frequency :                                                                       or                                                                        The...

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D Devendra Khairwa
Using Newton's second law of motion we can write :                                                                                                                                                   Also, the frictional force is given by :                                                                      or                                                                      Thus net force...

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D Devendra Khairwa
(b)  With reference to the observer moving with trolley, the trolley will be at rest as a pseudo force will act to balance out the frictional force. In relative motion both are moving together, thus are rest with respect to each other. 

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D Devendra Khairwa
(a) Using Newton's second law of motion we can write :                                 or                                    Its direction is in the direction of motion of trolley.                           The frictional force is      or                                                              Since the frictional force is greater than the applied force so the block will appear to be at...

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D Devendra Khairwa
Consider block A.       The frictional force on block A will be :                                   or                                      Thus net force on B due to block A is  =  200  -  7.5   = 192.5 N. The net force on the partition is 177.5 N. Using Newton's law of motion we have,                                    or                                For block A :                        ...

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D Devendra Khairwa
The applied force is 200 N. The maximum friction force on the system is given by :                                             or                                              So the net force on partition is  200  -  22.5  =  177.5  N. This will be equal to the reaction of the partition (action-reaction pair). The direction will be leftward. 

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D Devendra Khairwa
Given that   Tmax  =  600 N. (a)   Acceleration of  6 m s-2 in the upward direction:-                               Using Newton's law of motion we can write  :                                                               or                                                                Thus rope will break. (b)   Acceleration of 4 m s-2 in a downward direction:-                             ...

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D Devendra Khairwa
Using Newton's law force applied on the block:-             or                                                                                                                                                              Weight of man   =   500 N Case 1:-  When a man is lifting block directly, man is applying force in the upward direction directly.                            The net force on...

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D Devendra Khairwa
The required centripetal force is provided by the rails, as by Newton's third law of motion, wheels apply force on the rails and thus rails provides a force on the wheels (action-reaction pair). We know that the angle of banking is given by :                                                       or                                                                 or                               ...

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D Devendra Khairwa
Convert speed of aircraft in SI units :                                                              We are familiar with the following relation :                                                               or                                                                   or                                                                         or                                         ...

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D Devendra Khairwa
Since the 6th coin will experience a force due to 4 coins that are present above i.e., 4 mg. According to Newton's law of action-reaction pair, the 6th coin will have a reaction force on 7th coin of magnitude 4 mg in the upward direction.

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D Devendra Khairwa
The eighth coin is placed directly above the 7th coin. Thus the net force experienced by 7th coin is due to 8th coin (as the 7th coin is in contact with 8th coin only from the top). Hence the force on the 7th coin by the eighth coin is 3 mg.

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D Devendra Khairwa
The weight on the 7th coin is due to the top 3 coins. So required force is equal to the weight of 3 coins  =   3 mg This force is acting vertically downward.

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D Devendra Khairwa
Firstly we will calculate the mass of water passing through per second  :                                                      or                                                          or                                                          Force is defined as the rate of change of momentum.                                                      or                                           ...

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D Devendra Khairwa
       or                                                  or                                                         or                                                         The direction of the force of the rotor on the surrounding will be in the downward direction. By action-reaction pair, the force on helicopter due to the surrounding is 32500 N and it is directed vertically upward. 

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D Devendra Khairwa
(b) In this case, we need to consider helicopter and passengers in a system because we need to determine the action of the rotor.         So by Newton's laws motion, we have :                                                      or                                                  or                                                         or                                                     ...

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D Devendra Khairwa
(a) The normal force on the floor will be the reaction force due to crew and passengers.        Using Newton's laws of motion we can write :                                              Thus                                      or                                                  or                                                The direction of normal force on the floor will be vertically upward. 
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