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) = (K_(1))/(2)`
B. `K_(2) = 2K_(1)`
C. `K_(2) = K_(1)`
D. `K_(2) = (K_(1))/(4)`

Answer

B

Explanation

Maximum kinetic energy ` = (1)/(2) m omega ^(2) A^(2)`
`omega = sqrt(( g)/(L))`
`A = L theta`
`LE = (1)/(2) m (g)/( L) xx L^(2) theta ^(2) , KE = (1)/(2) ,mgL theta^(2)`
If length is doubled
`K^(2) = (1)/(2) mg (2L) theta ^(2) ` [ here we are assuming angular amplitude is same ]
`(K_(1))/( K_(2)) = ((1)/(2) mgl theta ^(2))/((1)/(2) mg ( 2L) theta ^(2)) = (1)/(2) rArr K_(2) = 2K_(1)`