Question

An expression of phisical quantity is written as X=√T/m where T is the applied force and m is t he mass per unit lenght.Find the dimenional representation of X and identify the physical quantity

Answer 1

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Mass per unit length means that  Mass/length = kg/m

Answer 2

The dimensional representation of X is $LT^{-1}$ and it shows velocity of an object.

Explanation:

An expression of physical quantity is written as :

$X=\sqrt{\dfrac{T}{m}}$

T is the tension, T = ma

m is the mass per unit length

$X=\sqrt{\dfrac{ma}{(M/l)}}$

Using dimensional formula of all the quantities

$X=\sqrt{\dfrac{[M][LT^{-1}]}{([M]/[L])}}$

$X=\sqrt{\dfrac{L^2}{T^2}}$

$X=\dfrac{L}{T}$

$X=LT^{-1}$

So, the dimensional representation of X is $LT^{-1}$ and it shows velocity of an object.

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