Two pendulums begin to swing simultaneously. The first pendulum makes nine full oscillations when the other makes seven. The ratio of the lengths of the two pendulum is

Step-by-step solution

As two pendulums begin two swings simultaneously, then n 1 T 1 = n 2 T 2 Where, n 1 and n 2 are the number of oscillations of first and second pendulum respectively and T 1 and T 2 be their respective time periods. The time period of simple pendulum is given by T = 2 π l g where, l =length of pendulum and g = acceleration due to gravity ⇒ T 2 ∝ 1 …. (ii) So, from Eqs. (i) And (ii), we get l 1 l 2 = T 1 2 T 2 2 = n 2 2 n 1 2 Here, n 1 = 9 , n 2 = 7 ⇒ l 1 l 2 = 7 2 9 2 49 81 Hence, the ratio of pendulum lengths l 1 :