Errors in Measurement

Assertion: When percentage errors in the measurement of mass and velocity are $1\%$ and $2\%$, respectively, the percentage error in Kinetic Energy is $5\%$. 

Reason:  $\frac{\Delta E}{E}=\frac{\Delta m}{m}+\frac{\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}2\Delta v}{v}$ (where $E$ is the kinetic energy, $m$ is the mass and $v$ is the velocity). 

The zero error is classified as:

End correction is a correction in : 

The end correction is :

In acoustics, end correction is a short distance applied or added to the actual length of a resonance pipe, in order to calculate the precise resonant frequency of the pipe.

What is end correction?

In an experiment time period of a simple pendulum are measured as $2.63 \mathrm{s},2.56 \mathrm{s}$, $2.71 \mathrm{s},2.80 \mathrm{s}$. Find average absolute error and the percentage error.

The length and width of a rectangular room are measured to be $3.95\pm 0.05 \mathrm{m}$ and $3.05\pm 0.05 \mathrm{m}$, respectively. The area of the floor is

The length of a simple pendulum is about $100 \mathrm{cm}$ known to have an accuracy of $1 \mathrm{mm}$. Its period of oscillation is $2 \mathrm{s}$, determined by measuring the time for $100$ oscillation using a clock of $0.1 \mathrm{s}$ resolution. What is the accuracy in the determined value of $g$?

In a Searle's experiment, the diameter of the wire as measured by a screw gauge is $0.050 \mathrm{cm}$. The pitch of screw gauge is $2 \mathrm{mm}$ and number of divisions on circular scale is $200$. The length, measured by a scale of least count $0.1 \mathrm{cm}$, is $100 \mathrm{cm}$. When a weight of $50 \mathrm{N}$ is suspended from the wire, the elongation is measured to be $0.125 \mathrm{cm}$ by a micrometer of least count $0.001 \mathrm{cm}$. Find the maximum percentage error in the measurement of Young's modulus of the material of the wire from these data. (Approximate the answer to the nearest integer.)

Mention the causes of personal errors.

How can parallax cause personal errors?

Personal errors can be caused due to

These errors are caused by an individual's carelessness while making proper observation

Define personal errors.

In a resonance tube experiment, a tuning fork resonates with an air column $10 \mathrm{cm}$ long and again resonates when it is $32.2 \mathrm{cm}$ long. Calculate the wavelength of wave and the end correction.

Show that for pipe open at both ends, the end correction is $e=\frac{n_2{l}_2-n_1{l}_1}{2(n_1-n_2)}$ where the symbols have their usual meanings.

Two organ pipes of the same length, open at both ends, produce sound of different frequencies, if their radii are different. Why?

A cube has numerically equal volume and surface area. What is the volume of such a cube?