The length of a pendulum is measured as 1.01 | vedclass

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

Question

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

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(C) The formula for the time period of a simple pendulum is $T = 2\pi \sqrt{\frac{l}{g}}$.Squaring both sides, we get $T^2 = 4\pi^2 \frac{l}{g}$, which implies $g = 4\pi^2 \frac{l}{T^2}$.The relative error in $g$ is given by $\frac{\Delta g}{g} = \frac{\Delta l}{l} + 2 \frac{\Delta T}{T}$.Given: $l = 1.01 \ m$, $\Delta l = 0.01 \ m$, $T_{total} = 63 \ s$, $\Delta T_{total} = 3 \ s$.The time period $T = \frac{T_{total}}{30} = \frac{63}{30} = 2.1 \ s$.The error in time period $\Delta T = \frac{\Delta T_{total}}{30} = \frac{3}{30} = 0.1 \ s$.Substituting these values into the error formula:$\frac{\Delta g}{g} = \frac{0.01}{1.01} + 2 	imes \frac{0.1}{2.1} \approx 0.0099 + 0.0952 \approx 0.1051$.Percentage error = $0.1051 	imes 100 \% \approx 10.5 \%$.Rounding to the nearest provided option, the percentage error is $10 \%$.

The length of a pendulum is measured as $1.01 \ m$ and the time for $30$ oscillations is measured as $1 \ minute \ 3 \ s$. The error in length is $0.01 \ m$ and the error in time is $3 \ s$. The percentage error in the measurement of acceleration due to gravity is: (in $\%$)

Similar Questions

Zero error of an instrument introduces

In an experiment for the measurement of $g$ using a simple pendulum,the time period was measured with an accuracy of $0.2 \%$ while the length was measured with an accuracy of $0.5 \%$. The percentage accuracy in the value of $g$ thus obtained is: (in $\%$)

$A$ physical quantity $S$ is related to four observables $a, b, c$, and $d$ as $S = \frac{\sqrt{a} b}{c^3 d^4}$. If the percentage errors of measurement in $a, b, c$, and $d$ are $2 \%$, $1 \%$, $1 \%$, and $1 \%$ respectively, then the percentage error in the quantity $S$ is: (in $\%$)

The percentage error in the measurement of mass and velocity are $3 \%$ and $4 \%$ respectively. The percentage error in the measurement of kinetic energy is (in $\%$)

The error in the measurement of length and mass of a cube is $3\%$ and $4\%$ respectively. The error in the measurement of its density will be (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module