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.
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