A pendulum is executing simple harmonic motion and its maximum kinetic energy is `K_(1)`. If the length of the pendulum is doubled and it perfoms simple harmonuc motion with the same amplitude as in the first case, its maximum kinetic energy is `K_(2)` Then:

Options

A. `K _(2)=2K _(1)`
B. `K _(2) =K_(1)`
C. `K _(2) = (K_(1))/(4)`
D. `K _(1) = (k_(1))/(2)`

Answer

D

Explanation

`KE_(max) = 1/2 m omega ^(2) A ^(2)`
`implies (K_(1))/(K _(2))= (omega _(1)^(2))/(omega _(2)^(2))or (K_(1))/(K _(2))=(g//L)/(g//2L)or K _(2) = (K_(1))/(2)`