In the expression for time period T of a simp | vedclass

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

Question

(D) The formula for the time period of a simple pendulum is $T = 2 \pi \sqrt{\frac{l}{g}}$.Squaring both sides,we get $T^2 = 4 \pi^2 \frac{l}{g}$.Rear

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(D) The formula for the time period of a simple pendulum is $T = 2 \pi \sqrt{\frac{l}{g}}$.Squaring both sides,we get $T^2 = 4 \pi^2 \frac{l}{g}$.Rearranging for $g$,we get $g = 4 \pi^2 \frac{l}{T^2}$.The relative error in $g$ is given by $\frac{\Delta g}{g} = \frac{\Delta l}{l} + 2 \frac{\Delta T}{T}$.To find the percentage error,multiply by $100$:$\frac{\Delta g}{g} 	imes 100 = \left( \frac{\Delta l}{l} 	imes 100 ight) + 2 \left( \frac{\Delta T}{T} 	imes 100 ight)$.Given $\frac{\Delta l}{l} 	imes 100 = 2 \%$ and $\frac{\Delta T}{T} 	imes 100 = 2 \%$.Substituting these values: $\frac{\Delta g}{g} 	imes 100 = 2 \% + 2(2 \%) = 2 \% + 4 \% = 6 \%$.

In the expression for time period $T$ of a simple pendulum $T = 2 \pi \sqrt{\frac{l}{g}}$,if the percentage error in time period $T$ and length $l$ are $2 \%$ and $2 \%$ respectively,then the percentage error in acceleration due to gravity $g$ is equal to ......... $\%$

Similar Questions

Time for $20$ oscillations of a pendulum is measured as $t_1 = 39.6\, s$,$t_2 = 39.9\, s$,and $t_3 = 39.5\, s$. What is the precision in the measurements? What is the accuracy of the measurement?

For $z = a^{2} x^{3} y^{1/2}$,where $a$ is a constant. If the percentage error in the measurement of $x$ and $y$ are $4\%$ and $12\%$,respectively,then the percentage error for $z$ will be $........... \%$.

In five successive measurements, the mass of a ball is measured to be $2.61 \,g, 2.58 \,g, 2.40 \,g, 2.73 \,g$ and $2.80 \,g$. The mean absolute error in the measurement is (in $\,g$)

$A$ body travels uniformly a distance of $(13.8 \pm 0.2) \text{ m}$ in a time $(4.0 \pm 0.3) \text{ s}$. Its velocity with error limits and percentage error is

If $f = x^2$,what is the relative error in $f$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module