Pendulum: Effect of Gravity
Compare on Earth, Moon, Mars, Jupiter.
Key Notes
Period of a pendulum T = 2π√(L/g) — inversely proportional to √g.
Smaller g (higher altitude, equator, Moon) ⇒ LONGER period.
Higher g (poles, Earth's center) ⇒ SHORTER period.
Pendulums historically used to measure g — extremely precise at ~10⁻⁵.
Pendulum at top of mountain runs SLOW: g drops by ~0.3% at 10 km altitude.
Pendulum at equator runs slightly slower than at poles due to Earth's rotation + oblateness.
On the Moon (g ≈ 1.6 m/s²): T_moon ≈ 2.45 × T_earth.
g measurement: g = 4π²L/T². Modern atom-interferometer measurements: g to 10⁻⁹ precision.
Formulas
Period vs g
Inverse-square-root in g.
Measuring g
Classic pendulum experiment.
Variation with altitude h
g decreases linearly at small h.
Ratio at different g
Useful for comparison.
Important Points
T ∝ 1/√g — same length pendulum is SLOWER where g is smaller.
On Moon: T_moon/T_earth = √(g_earth/g_moon) ≈ √(9.8/1.6) ≈ 2.47.
Pendulum clocks are calibrated for SPECIFIC g — moving them changes the rate.
Going up a tall building: g drops slightly ⇒ pendulum clock runs slow ⇒ behind by ~3 seconds/day at the top of a 1km tower.
Equator vs pole: g differs by ~0.5% ⇒ pendulum period differs by ~0.25%.
Atom interferometers now provide sub-ppm gravity measurements — based on matter waves.
Pendulum: Effect of Gravity notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.