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D Devendra Khairwa
Total energy = kinetic energy (KE) + potential energy(PE) KE > 0 since m and v2 is positive. If KE <0 particles cannot be find. If PE>TE, then KE<0 (now in all graph check for this condition) In case 1 kinetic energy is negative for x<a. So at x<a particle cannot be found. In case 2 for x<a and for x> b kinetic energy is negative. So the particle cannot be found in these regions. In the...

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D Devendra Khairwa
The potential energy of the system depends inversely on the separation between the balls. Thus the potential energy will decrease as the balls will come closer and will become zero as they touch each other. Thus elastic collision is best described only by the graph (v).  

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D Devendra Khairwa
The initial momentum of the system (boy + trolley) is given as :                                                                                                                                            Now assume v' is the final velocity of the trolley with respect to the ground. Then the final momentum will be :                                                         Conserving momentum :  ...

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D Devendra Khairwa
In this case, the heat produced is the loss in the potential energy.  Thus,            heat produced  =  mg h or                                            or                                            The heat produced (when the lift is stationary) will remain the same as the relative velocity of the bolt with respect lift still remains zero.

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D Devendra Khairwa
Displacement (x) of the block is given as :   =  0.1 m. Using equilibrium conditions we can write :                                                 and                                                                           (  is the frictional force). We can write work done in terms of potential energy as :                                            or                                     ...

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D Devendra Khairwa
The FBD of the track is shown in the figure below :                                                Using the law of conservation of energy we have :                                             or                                             Hence both stones will reach the bottom with the same speed. For stone 1 we can write :                                     or                               ...

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D Devendra Khairwa
We are given :                       Mass of the bullet m: 0.012 Kg      Mass of the block M: 0.4  Kg   The initial velocity of the bullet u: 70  m/s  The initial velocity of the block     :     0   The final velocity of the system (bullet + block): v For finding the final speed of system we will apply the law of conservation of momentum :                                     or                 ...

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D Devendra Khairwa
A typical has dimensions of  . The area of the roof of the house is . This is nearly equal to the area required for the production of the given amount of electricity.

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D Devendra Khairwa
It is given that the efficiency of energy conversion is 20 per cent. According to question, we can write (equating power used by family) :                                                                        (Here A is the area required.) or                                                    or                                                           Thus required area is 200 m2.

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D Devendra Khairwa
Efficiency is given to be 20 per cent. Thus energy supplied by the person :                                                      Thus the amount of fat lost is :                                                     or                                                                                                 

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D Devendra Khairwa
The work done against the gravitational force is given by :                                               =   Number of times the weight is lifted  work done in 1 time.                                               or                                           or                                          

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D Devendra Khairwa
It is given that 25 per cent of wind energy is converted into electrical energy. Thus electric energy produced is :                                                               or                                                 Now the electric power is given by  :                                                   or                                                                 or           ...

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D Devendra Khairwa
The kinetic energy is given by :                                                      or                                                 or                                               Thus the kinetic energy of wind is        J.

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D Devendra Khairwa
The volume of wind   =    here   is the swept circle and  is the velocity.  Thus the mass of the wind is  : -      ,     is the density of the air. Hence mass of wind flowing through windmill in time t is     .

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D Devendra Khairwa
The relation between work done and the kinetic energy is given by :                                      Using the relation     we can write :                        Initial velocity  =   0    (at x  =  0 ) And          the final velocity    =      (at  x  = 2). Thus work done is :                                       or                                                  or                     ...

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D Devendra Khairwa
Since the sand is falling in the trolley thus the force generated on the system (trolley and sandbag) is an internal force. There is no external force thus momentum of the system doesn't change. Hence speed remains the same i.e.,  27 Km/hr.

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D Devendra Khairwa
Consider the extreme position (horizintal) :-                        The kinetic energy at this position is zero as velocity is zero.                       Thus total energy is given by :     Now consider the mean position (lowermost point) :  Here the potential energy of bob is zero.                Whereas   kinetic energy is  :                                                                 ...

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D Devendra Khairwa
Mass of the water is :                                             or                                                 Thus the output power is given by :                                              or                                                          or                                                          or                                                          Also, we are given...

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D Devendra Khairwa
This is an elastic collision thus the transfer of momentum will take place. It is given that bob B is at rest and bob A has some velocity. So in momentum transfer, bob B will gain the velocity in the left direction whereas bob A will come to rest (complete momentum transfer takes place). Hence bob A will not rise.
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