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

Options

A. `10:7`
B. `5:7`
C. `7:10`
D. `2:5`

Answer

B

Explanation

Total kinetic energy of the sphere can be written as follows:
`K=K_(t)+K_(r)=(1)/(2)mv^(2)+(1)/(2)Iomega^(2)`
`=(1)/(2)mv^(2)+(1)/(2)xx((2)/(5)mr^(2))((v)/(r))^(2)`
`=(7)/(10)mv^(2)`
Note that total kinetic energy is sum of translational and rotational kinetic energies. We can rewrite total kinetic energy as follows:
`K_(t)+K_(r)=(7)/(5)((1)/(2)mv^(2))=(7)/(5)K_(t)`
`(K_(t))/(K_(t)+K_(t))=(5)/(7)`
Hence option (6) is correct.