Calculate percentage error in determination of time period of a pendulum
$T = 2 π \sqrt{\frac{l}{g}}$
where l and g are measured with $\pm 1 %$ and $\pm 2 %$ .

Question

Calculate percentage error in determination of time period of a $$pendulumT=2$$$$π$$lgwhere l and g are measured with ±$$1$$% and ±$$2$$%.

Infinity Learn · Accepted Answer

$$T=2$$$$π$$$$lgT=(2$$π$$)(l)+1/2(g)-1/2Taking$$ logarithm of both sides, we $$haveln(T)=ln(2$$π$$)+12(lnl)-12ln(g)$$  …… (i)Here$$, $$2$$π is a constant, therefore $$ln(2$$π$$) is also a constant.Differentiating Eq. (i), we $$have1TdT=0+121l(dl)-121g(dg)dTTmax=$$ maximum value of ±$$12dll$$∓$$12dgg=12dll+12dggThis$$ can also be written asΔTT×$$100max=12$$Δll×$$100+12$$Δgg×$$100or$$ percentage error in time $$period=$$±$$12($$ percentage error in $$l)+12($$ percentage error in $$g)=$$±$$12$$×$$1+12$$×$$2=$$±$$1.5$$%

Calculate percentage error in determination of time period of a pendulum
$T = 2 π \sqrt{\frac{l}{g}}$
where l and g are measured with $\pm 1 %$ and $\pm 2 %$ .

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Calculate percentage error in determination of time period of a pendulumT=2πlgwhere l and g are measured with ±1% and ±2%.

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Calculate percentage error in determination of time period of a pendulum
$T = 2 π \sqrt{\frac{l}{g}}$
where l and g are measured with $\pm 1 %$ and $\pm 2 %$ .