Question

An expression of physical quantity is written as X=T/m where T is the applied force and m is the mass per unit length. Find the dimensional representation of X and identify the physical quantity.

Answer 1

Hello friend

Here , it is given that
T is force it means it is equal to
I.e,

T = mass × acceleration
And its dimensional formula is

T = [M][L][T]^-2

And m is the mass per unit so

m = mass/length
m = [M][L]^-1

And x = T/m

Then dimensional formula of x is

x = [M][L][T]^-2/[M][L]-1
x = [L]^2/[T]^2

I think in this question under root over T/ m is missing

And if under root is mention then dimensional formula of x is

x=[L]/[T]

And the given quantity is velocity
I hope this may help u

Answer 2

Dear friend

As it is given that
x = T/m

And the dimensional formula of x can be written as
x = dimensional formula of T ÷ dimensional formula of m

As it is given that
T is the force and m is the mass per unit length

Then dimensional formula of T is
T= mass ×acceleration

So dimensional formula of T is [M][L][T]^-2

And as m is the mass per unit length. So its dimensional formula is
x = mass/length
And dimensional formula of x is [M][LT]^-1

So , dimensional formula of x is
x = [M][L][T]^-2/[M][L]^-1

x = [L]^2[T]^-2

Or

x = [L]^2/[T]^2

I think something is wrong in this question
And that one is under root is not mention on T/m

If it is so then dimensional formula of x is [L]/[T]
And physical quantity is velocity