A simple pendulum `A` and `a` homogeneous rod `B` hinged at its enda are released from horizontal position as shown in figure.

Options

A. The times period of swing of simple pendulum is greater than that of rod If `L = l`
B. The times period of swing of simple pendulum is equal to that of rod If `L = l`
C. The times period of swing of simple pendulum is greater than that of rod If `L = (2l)/(3)`
D. The times period of swing of swing of simle pendulum is equal to that of rod if `L = (2l)/(3)`

Answer

A, D

Explanation

from conversation of energy
for simple pendulum.
`(1)/(2) mL^(2)omega^(1^(2)) = mgLsin theta`
`:. omega_(1) = sqrt((2g)/(L)sin theta)`

For homogenous rod
`(1)/(2)((ml^(2))/(3)) omega^(2^(2)) = mg'(l)/(2)sin theta`
`omega_(2) = sqrt((3g)/(l) sintheta)`

when `L = (2)/(3)l, omega_(1) = omega_(2)` at all time
so time periods of swinf are equal.