A quantity $z$, to be estimated has a dependency on the variables $a, b$ and $c$ as $z=a b^{2} c^{-2}$. The percentage of error in the measurement of $a, b$ and $c$ are respectively, $2.1 \%, 1.3 \%$ and $2.2 \%$. The percentage of error in the measurement of $z$ would then be
- $5.6 \%$
- $1.6 \%$
- $1.0 \%$
- $9.1 \%$
The Correct Option is D
Solution and Explanation
So, the percentage error in the volume is given by
$\frac{\Delta z}{z} \times 100=\left[\frac{\Delta a}{a}+2 \frac{\Delta b}{b}+2 \frac{\Delta c}{c}\right] \times 100$
$=2.1 \%+2(1.3 \%)+2(2.2 \%)=9.1 \%$
Top Questions on Units and measurement
- The pitch of an error free screw gauge is 1 mm and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads 1 mm and 63rd division on the circular scale coincides with the reference line. The diameter of the wire is:
- NEET (UG) - 2024
- Physics
- Units and measurement
- The potential energy of a particle moving along the x-direction varies as:
\[ V = \frac{Ax^2}{\sqrt{x} + B} \]
The dimensions of \(\frac{A^2}{B}\) are:- NEET (UG) - 2024
- Physics
- Units and measurement
- Least count of a vernier caliper is \( \frac{1}{20N} \, \text{cm} \).The value of one division on the main scale is \(1 \, \text{mm}\). Then the number of divisions of the main scale that coincide with \(N\) divisions of the vernier scale is:
- JEE Main - 2024
- Physics
- Units and measurement
- Given below are two statements:
Statement (I): Dimensions of specific heat is $[L^{2}T^{-2}K^{-1}]$
Statement (II): Dimensions of gas constant is $[M L^{2}T^{-2}K^{-1}]$- JEE Main - 2024
- Physics
- Units and measurement
- In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^\text{th}$ division coincides exactly with a certain division on the main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm, then how many main scale divisions are there in 1 cm?
- JEE Main - 2024
- Physics
- Units and measurement
Questions Asked in TS EAMCET exam
The ratio of the radii of two solid spheres of same mass in 2:3. The ratio of the moments of inertia of the spheres about their diameters is:
- TS EAMCET - 2023
- rotational motion
If (-c, c) is the set of all values of x for which the expansion is (7 - 5x)-2/3 is valid, then 5c + 7 =
- TS EAMCET - 2023
- Algebra of Complex Numbers
The general solution of the differential equation (x2 + 2)dy +2xydx = ex(x2+2)dx is
- TS EAMCET - 2023
- Differential equations
If i=√-1 then
\[Arg\left[ \frac{(1+i)^{2025}}{1+i^{2022}} \right] =\]- TS EAMCET - 2023
- Trigonometric Identities
If nCr denotes the number of combinations of n distinct things taken r at a time, then the domain of the function g (x)= (16-x)C(2x-1) is
- TS EAMCET - 2023
- permutations and combinations
Concepts Used:
Units and Measurement
Unit:
A unit of a physical quantity is an arbitrarily chosen standard that is broadly acknowledged by the society and in terms of which other quantities of similar nature may be measured.
Measurement:
The process of measurement is basically a comparison process. To measure a physical quantity, we have to find out how many times a standard amount of that physical quantity is present in the quantity being measured. The number thus obtained is known as the magnitude and the standard chosen is called the unit of the physical quantity.
Read More: Fundamental and Derived Units of Measurement
System of Units:
- CGS system
- FPS system
- MKS system
- SI units
Types of Units:
Fundamental Units -
The units defined for the fundamental quantities are called fundamental units.
Derived Units -
The units of all other physical quantities which are derived from the fundamental units are called the derived units.