Download App

Units and Measurements — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsUnits and Measurements3 Marks
Question
A physical quantity P is related to four observables a, b, c and d as follows:$\text{P}=\text{a}^3\text{b}^3/\big(\sqrt{\text{c}}\text{ d}\big)$
The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?
✓

Answer

$\text{P}=\frac{\text{a}^3\text{b}^2}{(\sqrt{\text{c}}\text{ d})}$Maximum fractional error in P is given by
$\frac{\Delta\text{P}}{\text{P}}=\pm\Big[3\frac{\Delta\text{a}}{\text{a}}+2\frac{\Delta\text{b}}{\text{b}}+\frac{1}{2}\frac{\Delta\text{c}}{\text{c}}+\frac{\Delta\text{d}}{\text{d}}\Big]\\=\pm\Big[3\Big(\frac{1}{100}\Big)+2\Big(\frac{3}{100}\Big)+\frac{1}{2}\Big(\frac{4}{100}\Big)+\frac{2}{100}\Big]$
$=\pm\frac{13}{100}=\pm0.13$
Percentage error in $\text{P}=\frac{\Delta\text{P}}{\text{P}}\times100=\pm0.13\times100=\pm13\%$
Percentage error in P = 13%
Value of P is given as 3.763.
By rounding off the given value to the first decimal place, we get P = 3.8.

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 "3 Marks Question" 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

The mass and diameter of a planet are twice of those of the earth. What will be the period of oscillation of a pendulum on this planet, if it is a second's pendulum on the earth?
→
Consider the situation of the previous question from a frame moving with a speed $v_0$ parallel to the initial velocity of the block.
  1. What are the initial and final kinetic energies?
  2. What is the work done by the kinetic friction?
→
A hydraulic automobile lift is designed to lift cars with a maximum mass of $3000kg$. The area of cross-section of the piston carrying the load is $425cm^2$. What maximum pressure would the smaller piston have to bear?
→
A physical quantity P is related to four observables a, b, c and d as follows: $\text{P}=\text{a}^3\text{b}^3/\big(\sqrt{\text{c}}\text{ d}\big)$ The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?
→
In an experiment, it was found that the string vibrates in $3$ loops when 'x' g was as mass of placed on the scale pan. What must be placed on the pan to make the string vibrate in 9 loops?
→
Assume that each atom in a copper wire contributes one free electron. Estimate the number of free electrons in a copper wire having a mass of 6.4g (take the atomic weight of copper to be $64g ~mol^{-1}$.
→
An ideal gas expands from $100\ cm^3$ to $200\ cm^3$ at a constant pressure of $2.0 \times 10^5 Pa$ when $50J$ of heat is supplied to it. Calculate,
→
To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass $1000 \ kg$ moving with a speed $18.0 \ km / h$ on a smooth road and colliding with a horizontally mounted spring of spring constant $5.25 \times 10^3 N m ^{-1}$. What is the maximum compression of the spring?
→
A U-tube is made up of capillaries of bore 1 mm and 2 mm respectively. The tube is held vertically and partially filled with a liquid of surface tension 49 dyne $cm ^{-1}$ and zero contact angle. Calculate the density of the liquid, if the difference in the levels of the meniscus is 1.25 cm . Take $g =980 cms ^{-2}$.
→
State first law of thermodynamics. Why is $C_p>C_v$ ? Derive the relation $C_p-C_v=R$ for an ideal gas.
→