Download App

Units and Measurements — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements2 Marks
Question
A physical quantity X is given by: $\text{X}=\frac{\text{P}^2\text{Q}^{\frac{3}{2}}}{\text{R}^4\text{S}^{\frac{1}{2}}}$ The percentage errors in P, Q, R and S are 1%, 2%, 4% and 2%. Calculate the percentage error in X.
✓

Answer

The maximum fractional error in X is given by:$\frac{\Delta\text{X}}{\text{X}}=\pm\Big[\frac{2\Delta\text{P}}{\text{P}}+\frac{3}{2}\frac{\Delta\text{Q}}{\text{Q}}+\frac{4\Delta\text{R}}{\text{R}}+\frac{1}{2}\frac{\Delta\text{S}}{\text{S}}\Big]$
$\frac{\Delta\text{X}}{\text{X}}=\pm\Bigg[2\times\Big(\frac{1}{100}\Big)+\frac{3}{2}\Big(\frac{2}{100}\Big)+4\times\Big(\frac{4}{100}\Big)+\frac{1}{2}\times\Big(\frac{2}{100}\Big)\Bigg]$
$\frac{\Delta\text{X}}{\text{X}}=\pm\frac{2}{100}+\frac{3}{100}+\frac{16}{100}+\frac{1}{100}$
$=\pm\frac{22}{100}=\pm0.22$Percentage error in $\text{X}=\frac{\Delta\text{X}}{\text{X}}\times100$
$=\pm0.22\times100=\pm22%$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Units and Measurements→Units and Measurements — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A man of mass 50kg starts moving on the earth and acquires a speed of 1.8m/s. With what speed does the earth recoil? Mass of earth = $6 \times 10^{24}kg$.
→
What is wave? Mention those two properties of the medium due to which transmission of mechanical waves is possible in the medium?
→
The torque of the weight of any body about any vertical axis is zero. Is it always correct?
→
A body has a sense of weightlessness in a satellite revolving around the earth, why?
→
A heat engine takes heat $Q_1$ at a temperature of 500 K and gives heat $Q_2$ at a temperature of 300 K to the sink and does $8 \times 10^5$ joules of work. Calculate the magnitude of $Q_1$ and $Q_2$.
→
In Exercise, let us take the position of mass when the spring is unstreched as x = 0, and the direction from left to right as the positive direction of x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is:At the maximum compressed position.
In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?
→
An unruly demonstrator lifts a stone of mass 200g from the ground and throws it at his opponent. At the time of projection, the stone is 150cm above the ground and has a speed of 3.00m/s. Calculate the work done by the demonstrator during the process. If it takes one second for the demonstrator to lift the stone and throw, what horsepower does he use?
→
Name four fundamental forces in nature.
→
Is it necessary for the plane of the orbit of a satellite to pass through the centre of the earth?
→
In the figure, the blocks are in contact with each other $m_1=3 kg, m_2=1 kg$. A horizontal force $F = 4 \mathrm { N }$. How much force can be applied :(i) On $m_1$ from the right side,
(ii) On $m_2$ from the left side? What will be the contact force between the two blocks?
→