Question

Q1. Which of the following is a dimensional variable *

(a) density

(b) angle

(c) strain

(d) specific gravity

plz give verified answer​

Answer 1

Given : (a) density

(b) angle

(c) strain

(d) specific gravity

To Find :  Which  is a dimensional variable

Solution

density   = Mass / Volume  

=   M/L³

= ML⁻³

Hence density   is a dimensional variable

angle is Dimension less

strain  = ΔL/L   = Change in length / Length

= L/L

=  L⁰

Dimensionless

specific gravity is  ratio between the density of an object, and a reference substance

specific gravity = Density A / Density B    

Hence Dimensionless

density   is a dimensional variable in given options

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Answer 2

HELLO DEAR,

QUESTION. Which of the following is a dimensional variable *

(a) density

(b) angle

(c) strain

(d) specific gravity

SOLUTION:- dimensional variable are those physical quantities which have dimensions of the form [ M^a L^b T^c ].

To check ,

(a) Density:- we know that , density = mass / volume

⇒ density = M / L³

⇒ density = M L-³.

(b) Angle :- we know that angle have no dimension ,it is dimension less quantity.

(c) Strain :- It is also dimentionless quantity

strain = change in length / original length

strain = ΔL / L

strain = L / L

strain = L ^0

Which is dimentionlesd.

(d) Specific gravity :- It is the ratio of density of an object to the given object.

specific gravity = Density of A / Density of B

Its also dimensionless quantity.

Therefore ,density is a dimension variable quantity.

So, option (a) density is correct .

I HOPE IT'S HELP YOU DEAR,

THANKS.