Rotational Motion Question 93
Question: A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy $ \text{(}{K_t}\text{)} $ as well as rotational kinetic energy $ \text{(}{K_r}\text{)} $ simultaneously. The ratio $ {K_t}\text{:(}{K_t}\text{+}{K_r}\text{)} $ for the sphere is
Options:
A) 10 : 7
B) 5 : 7
C) 7 : 10
D) (4) 2 : 5
Show Answer
Answer:
Correct Answer: B
Solution:
-
[b]
$ {K_t}\text{=}\frac{1}{2}m{v^{2}} $
$ {K_t}\text{+}{K_r}\text{=}\frac{1}{2}mv^{2}+\frac{1}{2}|{{\omega }^{2}}=\frac{1}{2}mv^{2}+\frac{1}{2}( \frac{2}{5}mr^{2} ){{( \frac{v}{r} )}^{2}} $
$ =\frac{7}{10}mv^{2} $
