Question:
A certain body weighs $22.42\,g$ and has a measured volume of $4.7\,cc$. The possible error in the measurement of mass and volume are $0.01\,gm$ and $0.1\,cc$. Then maximum error in the density will be
A certain body weighs $22.42\,g$ and has a measured volume of $4.7\,cc$. The possible error in the measurement of mass and volume are $0.01\,gm$ and $0.1\,cc$. Then maximum error in the density will be
Updated On: Jun 25, 2024
- $22\%$
- $2\%$
- $0.2\%$
- $0.02\%$
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Density $\rho=\frac{mass \, m}{volume \, V} .....(i)$
Take logarithm to take base $e$ on the both sides of eqn $(i)$, we get
$ ln\rho=lnm-lnV .....(ii)$
Differentiate eqn $(ii)$, on both sides, we get
$ \frac{? \rho}{\rho}=\frac{? m}{m}-\frac{? V}{V}$
Errors are always added, Error in the density $\rho$ will be
$ =\big[\frac{? m}{m}+\frac{? V}{V}\big]\times100 \%$
$=\big[\frac{0.01}{22.42}+\frac{0.1}{4.7}\big]\times100 \%$
$=2 \%$
Take logarithm to take base $e$ on the both sides of eqn $(i)$, we get
$ ln\rho=lnm-lnV .....(ii)$
Differentiate eqn $(ii)$, on both sides, we get
$ \frac{? \rho}{\rho}=\frac{? m}{m}-\frac{? V}{V}$
Errors are always added, Error in the density $\rho$ will be
$ =\big[\frac{? m}{m}+\frac{? V}{V}\big]\times100 \%$
$=\big[\frac{0.01}{22.42}+\frac{0.1}{4.7}\big]\times100 \%$
$=2 \%$
Was this answer helpful?
4
0
Top Questions on Units and measurement
- What are the units of viscosity, intensity of wave, and pressure gradient?
- JEE Main - 2025
- Chemistry
- Units and measurement
- Given below are two statements: Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In light of the above statements, choose the correct answer from the options given below.
- JEE Main - 2025
- Physics
- Units and measurement
- A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be \( \frac{x}{100} \), where \( x \) is:
- JEE Main - 2025
- Physics
- Units and measurement
- Choose the correct statements:
(A) Weight of a substance is the amount of matter present in it.
(B) Mass is the force exerted by gravity on an object.
(C) Volume is the amount of space occupied by a substance.
(D) Temperatures below 0°C are possible in Celsius scale, but in Kelvin scale negative temperature is not possible.
(E) Precision refers to the closeness of various measurements for the same quantity. Choose the correct answer from the options given below:- JEE Main - 2025
- Chemistry
- Units and measurement
The ratio of the power of a light source \( S_1 \) to that of the light source \( S_2 \) is 2. \( S_1 \) is emitting \( 2 \times 10^{15} \) photons per second at 600 nm. If the wavelength of the source \( S_2 \) is 300 nm, then the number of photons per second emitted by \( S_2 \) is ________________ \( \times 10^{14} \).
- JEE Main - 2025
- Physics
- Units and measurement
View More Questions
Questions Asked in NEET exam
- Given below are two statements :
Statement I : Bone marrow is the main lymphoid organ where all blood cells including lymphocytes are produced.
Statement II : Both bone marrow and thymus provide micro environments for the development and maturation of T-lymphocytes.
In the light of above statements, choose the most appropriate answer from the options given below :- NEET (UG) - 2024
- Organ And Organ System
- The type of conservation in which the threatened species are taken out from their natural habitat and placed in special setting where they can be protected and given special care is called;
- NEET (UG) - 2024
- Biodiversity
- Given below are two statements:
Statement I: In C3 plants, some O2 binds to RuBisCO, hence CO, fixation is decreased.
Statement II: In C4 plants, mesophyll cells show very little photorespiration while bundle sheath cells do not show photorespiration.
In the light of the above statements, choose the correct answer from the options given below:- NEET (UG) - 2024
- respiration in plants
- Given below are two statements :
Statement I : In the nephron, the descending limb of loop of Henle is impermeable to water and permeable to electrolytes.
Statement II : The proximal convoluted tubule is lined by simple columnar brush border epithelium and increases the surface area for reabsorption.
In the light of the above statements, choose the correct answer from the option given below :- NEET (UG) - 2024
- Nephrons
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The potential (V) at any axial point, at 2 m distance(r) from the centre of the dipole of dipole moment vector\(\vec{P}\) of magnitude, 4 × 10-6 C m, is ± 9 × 103 V.
(Take \(\frac{1}{4\pi\epsilon_0}=9\times10^9\) SI units)
Reason R : \(V=±\frac{2P}{4\pi \epsilon_0r^2}\), where r is the distance of any axial point, situated at 2 m from the centre of the dipole.
In the light of the above statements, choose the correct answer from the options given below :- NEET (UG) - 2024
- Magnetic Field
View More Questions
Concepts Used:
Physical World
The physical world includes the complications of the natural world around us. It is a type of analysis of the physical world around us to understand how it works. The fundamental forces that control nature are:
- Gravitational Force is a universal force that exists as an outcome of mutual attraction between any two objects with respect to their masses.
- Electromagnetic Force can be understood as the force that is present between the charged particles. The force is stated by Coulomb’s law.
- Strong Nuclear Force is the force that ties the protons and neutrons in a nucleus. Of all the elemental forces in nature, a strong nuclear force is the strongest as its name suggests.
- Weak Nuclear Force can only be noticed in some of the nuclear processes such as the beta decay of the nucleus.