Total kinetic energy of a rolling solid spher of mass m with velocity is

Options

A. `(7)/(10)Mv^(2)`
B. `(5)/(6)Mv^(2)`
C. `(7)/(5)Mv^(2)`
D. `(10)/(7)Mv^(2)`

Answer

A

Explanation

Total kinetic energy = Translational KE + Rotational KE
`=(1)/(2)mv^(2)+(1)/(2)l omega^(2)`
`=(1)/(2)mv^(2)+(1)/(2)((2)/(5)mR^(2))((v)/(R))^(2)`
`{{:(because" moment of inertia of sphere about its centre of mass"),(" "l=(2)/(5)mR^(2)):}}`
`" "=(1)/(2)mv^(2)+(1)/(5)mv^(2)=(7)/(10)mv^(2)`