A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy , (Kr) simultaneously. The ratio Kt: (Kt + Kr) for the sphere is

Question

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt) as well as rotational kinetic energy , (Kr) simultaneously. The ratio Kt: (Kt + Kr) for the sphere is (A) 2: 5 (B) 7: 10 (C) 10: 7 (D) 5: 7

Tardigrade Admin · Accepted Answer

Kt = (1/2) mv2 Kt +Kr = (1/2) mv2 + (1/2) I ω2 = (1/2) mv2 + (1/2) ((2/5) mr2)((v/r))2 = (7/10) mv2 So, (Kt/Kt + Kr ) = (5/7)

Q. 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

2 : 5

7 : 10

10 : 7

5 : 7

$K_{t} = \frac{1}{2} m v^{2}$
$K_{t} + K_{r} = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2} = \frac{1}{2} m v^{2} + \frac{1}{2} (\frac{2}{5} m r^{2}) (\frac{v}{r})^{2}$
$= \frac{7}{10} m v^{2}$
So, $\frac{K _{t}}{K _{t} + K _{r}} = \frac{5}{7}$

Q. A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy (Kt​) as well as rotational kinetic energy , (Kr​) simultaneously. The ratio Kt​:(Kt​+Kr​) for the sphere is