If the length of the pendulum in a pendulum c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{\ell}{g}}$.Taking the logarithmic derivative,we get $\frac{\Delta T}{T} = \

Vedclass · Accepted Answer

$43.2$

Vedclass · Answer

(C) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{\ell}{g}}$.Taking the logarithmic derivative,we get $\frac{\Delta T}{T} = \frac{1}{2} \frac{\Delta \ell}{\ell}$.Given that the length increases by $0.1\, \%$,so $\frac{\Delta \ell}{\ell} = \frac{0.1}{100} = 10^{-3}$.The error in time per day $(\Delta T)$ is calculated as $\Delta T = \frac{1}{2} 	imes \left( \frac{\Delta \ell}{\ell} ight) 	imes T_{total}$,where $T_{total} = 24 	imes 3600 \, s$.Substituting the values: $\Delta T = \frac{1}{2} 	imes 10^{-3} 	imes 86400 = 43.2 \, s$.

If the length of the pendulum in a pendulum clock increases by $0.1\, \%$,then the error in time per day is: (in $s$)

Similar Questions

The time period of a simple pendulum is $2 \, sec$. If its length is increased $4$ times,then its period becomes ..... $\sec$.

The bob of a simple pendulum is hanging vertically down from a fixed identical bob by means of a string of length $l$. If both bobs are charged with a charge $q$ each,what is the time period of the pendulum? (Ignore the radii of the bobs.)

The bob of a simple pendulum of mass $m$ and total energy $E$ will have maximum linear momentum equal to

The length of a seconds pendulum is .... $cm$.

If the length of a seconds pendulum becomes $\frac{1}{3}$ of its original length,what will be its new periodic time?

Vedclass Test Series

Exam Paper Generator

Online Exam Module