6. Which of the following exerts a small but measurable effect on the period of a real
clock pendulum? X: The amplitude of the pendulum swing. Y: The temperature.
Z: Buoyancy due to atmospheric pressure
a. X only
b. X and Y but not Z
c. Y and Z but not X
d. X and Y and Z
Effect of Amplitude Temperature Buoyancy on Real Clock Pendulum Period
✅ Correct Answer: b. X and Y but not Z
The period of a real clock pendulum deviates slightly from the ideal simple harmonic motion formula T = 2π √(L/g) due to non-ideal factors. For small angles, amplitude has negligible impact, but larger swings introduce measurable lengthening from nonlinear restoring forces.Temperature causes thermal expansion of the pendulum rod, increasing effective length L and thus period, a known issue in precision clocks. Buoyancy from air (tied to density, not directly pressure alone) exists but stems from constant average air density around sea level, yielding no measurable daily variation for clocks; pressure-driven changes are too minor (~0.015 s/day per torr).
🔍 Option Analysis
X (Amplitude)
Affects period measurably at larger angles (>5-10°) due to sinθ ≈ θ approximation failing, lengthening T slightly in real clocks with 2-4° swings.
Y (Temperature)
Increases L via ΔL = L α ΔT (α ∼ 10⁻⁵/°C), raising T by ~0.5 α ΔT fractionally; clocks slow ~1-8 s/day per 10°C rise.
Z (Buoyancy due to atmospheric pressure)
Reduces effective g via Archimedes but constant at typical pressures; barometric shifts cause trivial ΔT (~0.1 s/day/kPa), not “measurable” in standard clocks.
📝 Question Reference
6. Which of the following exerts a small but measurable effect on the period of a real clock pendulum?
X: The amplitude of the pendulum swing. Y: The temperature. Z: Buoyancy due to atmospheric pressure
a. X only | b. X and Y but not Z | c. Y and Z but not X | d. X and Y and Z
🎯 CSIR NET Physics Exam Tip
- Key Concept: Real pendulums deviate from ideal SHM due to finite amplitude, thermal expansion, and environmental effects
- Amplitude Effect: Period increases as T ≈ T₀(1 + θ₀²/16) for angle θ₀
- Temperature Compensation: Precision clocks use Invar rods (low α) or mercury jar pendulums
- Buoyancy: Negligible for typical clock bobs (~1-2% mass correction, constant effect)
