A solid sphere of mass `m` and radius `R` rolls without slipping on a horizontal surface such that `v_(c.m.)=v_(0)`.

Options

A. The kinetic energy of rotation is `(1)/(5)mv_(0)^(2)`.
B. The total kinetic energy is `(7)/(10)mv_(0)^(2)`.
C. The mechanical energy (assume the ground as reference) is `mgR+(7)/(10)mv_(0)^(2)`.
D. All options are correct.

Explanation

For sphere, `(k^(2))/(R^(2))=(2)/(5)`
`K_(R)=(k^(2))/(R^(2))xx(1)/(2)mv_(c.m.)^(2)=(2)/(5)xx(1)/(2)mv_(0)^(2)=(1)/(5)mv_(0)^(2)`
`K=(1+(k^(2))/(R^(2)))(1)/(2)mv_(c.m.)^(2)=(1+(2)/(5))xx(1)/(2)mv_(0)^(2)=(7)/(10)mv_(0)^(2)`
`U=mgR`
`E=K+U=(7)/(10)mv_(0)^(2)+mgR`