Practicing Success
If the length of a simple pendulum is decreased by 3%, the percentage change in its period T is : [Note : $T=2\pi \sqrt{\frac{L}{g}}$ where L is the length of pendulum and g is constant' |
1.5% decrease 1.8% decrease 2% increase 2.5% increase |
1.5% decrease |
The correct answer is Option (1) → 1.5% decrease $T=2\pi \sqrt{\frac{L}{g}}$ $ΔT=ΔL\frac{dT}{dL}$ $ΔT=\frac{3}{100}L×\frac{1}{2}×\frac{2π}{\sqrt{Lg}}$ $ΔT=\frac{1.5}{100}×2π\sqrt{\frac{L}{g}}$ so $\frac{ΔT}{T}=\frac{1.5}{100}$ so $\frac{ΔT}{T}×100=1.5\%$ |