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

A solid sphere is in rolling motion. In rolling motion a body possesses translational kinetic energy `(K_(t))` simultaneously. The ratio `K_(1):(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_(r)=(1)/(2)Iomega^(2)=(1)/(2)((2)/(5)mr^(2)).((v)/(r))^(2)=(1)/(5)mv^(2)`
`:. (K_(1))/(K_(t)+K_(r))=((1)/(2)mv^(2))/((1)/(2)mv^(2)+(1)/(5)mv^(2))=((1)/(2)mv^(2))/((7)/(10)mv^(2))=(5)/(7)`
or, `K_(t) : (K_(t) +K_(r)) = 5:7`
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