Question

The ratio of kinetic energy to the potential energy of a particle executing S.H.M. at a distance equal to (1/3)rd of its amplitude is ______.

Options

• 9 : 1

• 2 : 1

• 8 : 1

• 3 : 1

Answer 1

The ratio of kinetic energy to the potential energy of a particle executing S.H.M. at a distance equal to (1/3)rd of its amplitude is 8 : 1.

Explanation:

KE = `1/2 "m"omega^2("a"^2 - x^2)`

`= 1/2 "m"omega^2("a"^2 - "a"^2/9)`

`= 1/2 "m"omega^2 (8"a")^2/9`

PE = `1/2 "m"omega^2x^2`

`= 1/2 "m"omega^2 "a"^2/9`

`therefore "KE"/"PE"` = 8