Two simple pendulums ( A ) and ( B ) are made to oscillate simultaneously and it is found that ( A ) completes ( 10 ) oscillations in ( 20 sec ) and ( B ) completes ( 8 ) oscillations in ( 10 sec ). The ratio of the lengths of ( A ) and ( B ) is

Step-by-step solution

Time period of oscillations of a simple pendulum is given as ( T=2 l g ) where ( I ) is length of pendulum. For pendulum A: Given, completes ( 10 ) oscillations is ( 20 ~s ). Therefore, time period of single oscillation ( = 20 10 =2 ) [ array l T_ A =2 2 I_ A g =2 (1) array ] For pendulum B: Given, completes ( 8 ) oscillations in ( 10 ~s ). Therefore, time period of single oscillation ( = 10 8 = 5 4 ) [ array l T_ B = 5 4 2 l_ B g = 5 4 (2) array ] Divide Eq. (1) by Eq. (2), we get [ aligned & 2 l_ A g 2 & l_ B g =