A solid sphere is in rolling motion . In rolling motion a body possesses translational kinetic energy `(K_(t))` as well as rotational kinetic energy `(K_(r))` simultaneously . The ratio `K_(t) : (K_(t) + K_(r))` for the sphere is

Options

A. `7 : 10`
B. `5 : 7`
C. `10 : 7`
D. `2 : 5`

Answer

B

Explanation

Translational kinetic energy , `K_(t) = (1)/(2) mv^(2)`
Rotational kinetic energy `K_(r) = (1)/(2) I omega^(2)`
`therefore K_(t) + K_(r) = (1)/(2) m v^(2) + (1)/(2) I omega^(2) = (1)/(2) mv^(2) + (1)/(2) ((2)/(5) mr^(2)) ((v)/(r))^(2)`
`therefore K_(t) + K_(r) = (7)/(10) mv^(2) [ because I = (2)/(5) mr^(2)` (for sphere)]
So , `(K_(t))/(K_(t) + K_(r)) = (5)/(7)`