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Gundoos 1234 Grade: 11
        

A body of mass m moving with velocity u collides with another ball of mass m2 at rest. the ratio m1/m2 for maximum energy transfer is:


ans:1


 


in the worked out solution:


ΔK.E/K.E has been worked out as 4n/(1+n)^2


where n=m1/m2 and ΔK.E is decrease in K.E.


then, d/dn(4n/(1+n)^2) = 0


so n=1


 


can you please explain the differentiation part?


Is there any other method?

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

change of KE /KE = 4n/(n+1)2 or


change in KE depend upon 4n/(n+1)2        for a particular value of initial KE...


this means dKE is a function of n                 (where n is variable...)


now we have to maximise this change for this we can use concept of maxima & minima ...


dKE = f(n) = 4n/(n+1)2


 differentiating this eq wrt n


      d/dn [f(n)] = d/dn [4n/(n+1)2 ]


                     =4[-n2 + 1]/(n+1)4                           (using quotient rule)


  now putting the above expression equal to 0


             -n2+1 = 0


                  n=+1 or -1


now we have two values for n ,on substituting these values we will see that function


 is maximum at n=1 & minimum at n=-1 so n=1 is the value for which kinetic energy transferred is maximum...

6 years ago
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