Two pendulum clocks start simultaneously; only one keeps correct time. They swing in phase again for the first time at about the 100th swing. Find the approximate percentage change in the inaccurate pendulum's length needed to correct its period. [The source does not specify whether it runs fast or slow.]
Physics · Mixed Chapter
JEE Mains

Question

Two pendulum clocks start simultaneously; only one keeps correct time. They swing in phase again for the first time at about the 100th swing. Find the approximate percentage change in the inaccurate pendulum's length needed to correct its period. [The source does not specify whether it runs fast or slow.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — The period of a simple pendulum is T = 2π√(l/g). For a small length change, ΔT/T ≈ ½(Δl/l). Step 2 — If two close pendulums begin in phase, their next common phase after around 100 swings corresponds to one extra (or one fewer) swing of the inaccurate pendulum relative to the correct clock. Step 3 — Thus the magnitude of the relative period difference is approximately 1/100 = 1%. Step 4 — By the period–length relation, |Δl/l| ≈ 2|ΔT/T| ≈ 2%. Hence the printed approximate answer is 2. A…