Q. Two simple pendulum of length 0.5 m and 20 m respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed… oscillations.
A) 5
B) 1
C) 2
D) 3
Explanation
(a) Let $T_{1},T_{2}$ be the time period of shorter length and longer length pendulums respectively. Ads per question, $nT_{1} = (n - 1)T_{2}$;
So $n2\pi\sqrt{\frac{0.5}{g}} = (n - 1)2\pi\sqrt{\frac{20}{g}}$
or $n = (n - 1)\sqrt{40} \approx (n - 1)6$
Hence, $5n = 6$
Hence, after 5 oscillations they will be in same phase
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.