A solid sphere of radius r r is rolling on a horizontal surface. The ratiobetween the rotational kinetic energy and total energy.

A solid sphere of radius r r is rolling on a horizontal surface. The r

1.	A solid sphere of radius r r is rolling on a horizontal surface. The ratiobetween the rotational kinetic energy and total energy.
Answer» `(5)/(7)` `(2)/(7)` `(1)/(2)` `(1)/(7)` Solution :The rotation kinetic energy, `K_(r)=(1)/(2)IOMEGA^(2)` where, `I=` moment of inertia of solid sphere. The TOTAL kinetic energy and translational kinetic energy `K_(T)=(1)/(2)mv^(2)+(1)/(2) Iomega^(2)` `=(1)/(2)m omega^(2)r^(2)+(1)/(2) I omega^(2)""( :. "For pure rolling" v=omegar)` Now, `(K_(r))/(K_(T))=((1)/(2)I omega^(2))/((1)/(2) omega^(2)(mr^(2)+I))=(I)/(mr^(2)+I)` As `I=(2)/(5)mr^(2)`(for solid sphere) `RARR(K_(r))/(K_(T))=((2)/(5)mr^(2))/(mr^(2)+(2)/(5)mr^(2))=((2)/(5)mr^(2))/((7)/(5)mr^(2))=(2)/(5)XX(5)/(7)=(2)/(7)`.