The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt {\frac{l}{g}} $ where $l$ is about $100 \,cm$ and is known to have $1\,mm$ accuracy. The period is about $2\,s$. The time of $100$ oscillations is measured by a stop watch of least count $0.1\, s$. The percentage error in $g$ is ......... $\%$
The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt {\frac{l}{g}} $ where $l$ is about $100 \,cm$ and is known to have $1\,mm$ accuracy. The period is about $2\,s$. The time of $100$ oscillations is measured by a stop watch of least count $0.1\, s$. The percentage error in $g$ is ......... $\%$
- A
$0.1$
- B
$1$
- C
$0.2$
- D
$0.8$
Similar Questions
The relative error in resistivity of a material where
resistance $= 1.05 \pm 0.01\, \Omega$
diameter $= 0.60 \pm 0.01\, mm$
length $= 75.3 \pm 0.1 \,cm$ is
The relative error in resistivity of a material where
resistance $= 1.05 \pm 0.01\, \Omega$
diameter $= 0.60 \pm 0.01\, mm$
length $= 75.3 \pm 0.1 \,cm$ is
Students $I$, $II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum.
They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length $=0.1 \mathrm{~cm}$
Least count for time $=0.1 \mathrm{~s}$
Student
Length of the pendulum $(cm)$
Number of oscillations $(n)$
Total time for $(n)$ oscillations $(s)$
Time period $(s)$
$I.$
$64.0$
$8$
$128.0$
$16.0$
$II.$
$64.0$
$4$
$64.0$
$16.0$
$III.$
$20.0$
$4$
$36.0$
$9.0$
If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,
Students $I$, $II$ and $III$ perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum.
They use different lengths of the pendulum and /or record time for different number of oscillations. The observations are shown in the table.
Least count for length $=0.1 \mathrm{~cm}$
Least count for time $=0.1 \mathrm{~s}$
| Student | Length of the pendulum $(cm)$ | Number of oscillations $(n)$ | Total time for $(n)$ oscillations $(s)$ | Time period $(s)$ |
| $I.$ | $64.0$ | $8$ | $128.0$ | $16.0$ |
| $II.$ | $64.0$ | $4$ | $64.0$ | $16.0$ |
| $III.$ | $20.0$ | $4$ | $36.0$ | $9.0$ |
If $\mathrm{E}_{\mathrm{I}}, \mathrm{E}_{\text {II }}$ and $\mathrm{E}_{\text {III }}$ are the percentage errors in g, i.e., $\left(\frac{\Delta \mathrm{g}}{\mathrm{g}} \times 100\right)$ for students $\mathrm{I}, \mathrm{II}$ and III, respectively,
- [IIT 2008]
The relative error in the measurement of the side of a cube is $0.027$. The relative error in the measurement of its volume is ..........
The relative error in the measurement of the side of a cube is $0.027$. The relative error in the measurement of its volume is ..........
In an experiment of simple pendulum time period measured was $50\,sec$ for $25$ vibrations when the length of the simple pendulum was taken $100\,cm$ . If the least count of stop watch is $0.1\,sec$ . and that of meter scale is $0.1\,cm$ then maximum possible error in value of $g$ is .......... $\%$
In an experiment of simple pendulum time period measured was $50\,sec$ for $25$ vibrations when the length of the simple pendulum was taken $100\,cm$ . If the least count of stop watch is $0.1\,sec$ . and that of meter scale is $0.1\,cm$ then maximum possible error in value of $g$ is .......... $\%$
The period of oscillation of a simple pendulum is $T=2\pi \sqrt {\frac{l}{g}} $. Measured value of $L$ is $20.0\; cm$ known to $1\; mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90\ s$ using a wrist watch of $1\; s$ resolution. The accuracy in the determination of $g$ is ........ $\%$
The period of oscillation of a simple pendulum is $T=2\pi \sqrt {\frac{l}{g}} $. Measured value of $L$ is $20.0\; cm$ known to $1\; mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90\ s$ using a wrist watch of $1\; s$ resolution. The accuracy in the determination of $g$ is ........ $\%$
- [JEE MAIN 2015]