Question

The increasing order of fraction of total kinetic energy associated with translatory motion of the following rolling bodies is:
I) Circular ring
II) Circular plate
III) Solid sphere
IV) Hollow sphere

• A. $I,II,IV,III$
• B. $IV,I,II,III$
• C. $I,IV,II,III$
• D. $IV,I,III,II$

Answer 1

The correct option is C $I,IV,II,III$

fraction $=\frac{KE{)}_T}{KE{)}_T+KE{)}_R}$
$\frac{K_T+K_R}{K_T}$
$=\frac{\frac{1}{2}m{V}^2+\frac{1}{2}I(\frac{V}{R}{)}^2}{\frac{1}{2}m{V}^2}$
$I\uparrow$ fraction $\uparrow$
$I_{ring}>I_{H.Sphere}>I_{plate}>I_{S.Sphere}$