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 $T^2 = 4\pi^2 \frac{l}{g}$,which

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: $l = 1.01 \ m$,$\Delta l = 0.01 \ m$,$t_{total} = 63 \ s$,$\Delta t = 3 \ s$.The time period $T = \frac{t_{total}}{30} = \frac{63}{30} = 2.1 \ s$.The error in time period $\Delta T = \frac{\Delta t}{30} = \frac{3}{30} = 0.1 \ s$.Substituting these values into the error formula:$\frac{\Delta g}{g} = \frac{0.01}{1.01} + 2 \left( \frac{0.1}{2.1} ight) \approx 0.0099 + 0.0952 \approx 0.1051$.Converting to percentage: $\frac{\Delta g}{g} 	imes 100 \% \approx 10.51 \% \approx 10 \%$.

The length of a pendulum is measured as $1.01 \ m$ and the time for $30$ oscillations is measured as $1 \ \text{minute} \ 3 \ s$. 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:

Similar Questions

$A$ thermodynamic system is taken through the cycle $PQRSP$ as shown in the $PV$ diagram. The net work done by the system is...... $J$. (Note: $1 \text{ kp} = 10^3 \text{ Pa}$,$1 \text{ cc} = 10^{-6} \text{ m}^3$)

The electrons identified by quantum numbers $n$ and $l$: $(i)$ $n = 4, l = 1$; $(ii)$ $n = 4, l = 0$; $(iii)$ $n = 3, l = 2$; $(iv)$ $n = 3, l = 1$ can be placed in order of increasing energy from the lowest to highest,as

The experimentally determined molar mass of a non-volatile solute,$BaCl_2$,in water by Cottrell's method,is

Which of the following crops have been brought to India from the New World?

The solution of the differential equation $\frac{dy}{dx} = \sin(x+y) \tan(x+y) - 1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module