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Check the correctness of the relation : ...

Check the correctness of the relation :
`v=sqrt((E )/(rho))`
where the symbols have their usual meanings.

Text Solution

Verified by Experts

Dimensional formula of velocity `[v]=LT^(-1)`.
Dimensional formula of modulus of elasticity, `[E]=ML^(-1)T^(-2)`.
and dimensional formula of density, `[rho]=ML^(-3)`
Substituting the dimensional formula of all terms in the given relation, we have
`(LT^(-1))=((ML^(-1)T^(-2))/(ML^(-3)))^(1//2)` or `(LT^(-1))=(LT^(-1))`
Since dimensions of both sides are equal , so relation is correct.
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