First slide
Conservation of mechanical energy
Question

A particle is moving in a circle of radius ‘r’ under the action of a forceF=  αr2,  which is directed towards centre of the circle.  Total mechanical energy of the particle is (take P.E.  =  0    at  r = 0)
 

Moderate
Solution

Centripetal force   F=  αr2  
    mv2r   =    αr2      mv2   =    αr3   
   K.E.   =    12mv2    =   12  αr3   
    P.E.   =   U =F.dr PE=  αr2dr PE=    αr33  
      Total energy =P.E.  +K.E substitute above obtained values,  TE  =   αr33+  12  αr3 TE=56  αr3     
                                                                                       
 

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