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If a composite physical quantity in term...

If a composite physical quantity in terms of moment of inertia I, force F, velocity v, work W and length L is defined as,
`Q = (IFv^(2)//WL^(3))`,
find the dimensions of Q and identify it.

Text Solution

Verified by Experts

As `[I]=[ML^(2)]," "[F]=[MLT^(-1)]`
`[v]=[LT^(-1)]" "and" "[W]=[ML^(2)T^(-2)]`
`[Q]=([ML^(2)][MLT^(-2)][LT^(-1)]^(2))/([ML^(2)T^(-2)][L]^(3))`
`[Q]=[MT^(-2)]`
As `[MT^(-2)]` are dimensions of surface tension, force constant or surface energy, i.e., energy per unit area, the physical quantity may be any one of these.
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