### NEET Solved Paper 2018 Question 41

##### 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 [NEET - 2018]

#### Options:

A) 10 : 7

B) 5 : 7

C) 7 : 10

D) 2 : 5

## Show Answer

#### Answer:

Correct Answer: B

#### Solution:

$ {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} $

So, $ \frac{K _{t}}{K _{t}+K _{r}}=\frac{5}{7} $