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A solid sphere is in rolling motion. In ...

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

A

`10:7`

B

`5:7`

C

`7:10`

D

`2:5`

Text Solution

Verified by Experts

The correct Answer is:
B
`K_(t)=(1)/(2)mv^(2)`
`K_(t)+K_(r)=(1)/(2)mv^(2)+(1)/(2)Iomega^(2) =(1)/(2) mv^(2)+(1)/(2)((2)/(5)mr^(2))((v)/(r))^(2)`
`=(7)/(10)mv^(2)`
So, `(K_(t))/(K_(t)+K_(r))=(5)/(7)`
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