Question

(A) Specific gravity of a fluid is a dimensionless quantity $(R)$. It is the ratio of density of fluid to density of water. (A) Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$ (B) Both $A$ and $R$ are correct but $R$ is not the correct explanation of $A$ (C) $A$ is correct but $R$ is false (D) Both $A$ and $R$ are false

Name: Problem 58, Chapter 1: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-08T13:53:00-08:00
Duration: 1 min 29 s
Channel: Akshaya Rs
Description: (A) Specific gravity of a fluid is a dimensionless quantity (R). It is the ratio of density of fluid to density of water. (A) Both A and R are correct and R is the correct explanation of A (B) Both A and R are correct but R is not the correct explanation of A (C) A is correct but R is false (D) Both A and R are false

   (A) Specific gravity of a fluid is a dimensionless quantity $(R)$. It is the ratio of density of fluid to density of water.
(A) Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$
(B) Both $A$ and $R$ are correct but $R$ is not the correct explanation of $A$
(C) $A$ is correct but $R$ is false
(D) Both $A$ and $R$ are false

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 1, Problem 58

Instant Answer

Solved by Expert Akshaya Rs

10/08/2021

Step 1

By definition, specific gravity is the ratio of the density of a fluid to the density of water. Mathematically, it can be represented as: \[ SG = \frac{\rho_{fluid}}{\rho_{water}} \] where $ SG $ is the specific gravity, $ \rho_{fluid} $ is the density of the Show more…

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(A) Specific gravity of a fluid is a dimensionless quantity $(R)$. It is the ratio of density of fluid to density of water. (A) Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$ (B) Both $A$ and $R$ are correct but $R$ is not the correct explanation of $A$ (C) $A$ is correct but $R$ is false (D) Both $A$ and $R$ are false

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Key Concepts

Specific Gravity

Specific gravity is a measure of the relative density of a substance compared to a reference substance, typically water. It is calculated as the ratio of the density of the substance to the density of water, resulting in a number without units.

Dimensionless Quantity

A dimensionless quantity is one that has no physical units, meaning its value is independent of the measurement system used. In the case of specific gravity, the units cancel out when taking the ratio of two densities, leaving a pure number.

Density

Density is defined as mass per unit volume of a substance. It is a fundamental property in physics and engineering, and plays a critical role in determining specific gravity when comparing a substance to water.

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