Question

Which of the following have maximum percentage of total K.E. in rotational form while pure rolling – Disc, Sphere, Ring or Hollow sphere. PLZ  EXPLAIN  ALSO.

Joshi sir comment

total kinetic energy of a rolling body = mv2/2 + Iω2/2 = mv2/2 + Iv2​/2r2 = (mv2/2)[1+I/mr2

rotational kinetic energy of a rolling body =  Iω2/2 = Iv2​/2r2 = (mv2/2)[I/mr2

so ratio R. K. E. / T. K. E. =  (mv2/2)[I/mr2] /  (mv2/2)[1+I/mr2] = [I/mr2] / [1+I/mr2]

                                                                                          = [I/I+mr2

                                                                                          = 1/[1+(mr2/I)]

I is max. for a ring so ratio will be max. for a ring

 

  

 

Read 1 Solution.

total ke = ke translatory + rotational = 1/2mv^2  + 1/2 iω^2   now put w= v/r  and i= mK^2   now kE total will be proportional to 1+k2/r2  now find which one has this k^2/r^2  ratio higest  , disc= 1/2,  sphere if solid 2/5 if hollow2/3  ring= 1       thus  ans is  ring            

SARIKA SHARMA 10 year ago is this solution helpfull: 14 1

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