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Find the dimensional formula of the fo...

Find the dimensional formula of the following question :
(a) Density (b) Velocity (c) Acceleration (d) Momentum (e) Force (f) Work of energy (g) Power (h) Pressure

Text Solution

Verified by Experts

(a ) Density = (mass)/(volume)
[Density ] = ([mass])/([volume]) = `([M])/([L^(-3)]) = [ML^(-3)]`
(b) volume [v] = (displacement)/ (time)(b)volume `[v]` = (displacement)/ (time)
`[V]` = (displacement)/ (time) = `([L])/([T]) = [M^(0)LT^(-1)]` (c) `"Acceleration" [a] = ([dv)]/([dt)]`
`[e] = (dvrarr "kind of velocity")/(dt rarr "kind of time") = ([LT^(-1)])/([T]) = [LT^(-2)]`
(d) Momention `[P]= [mv]`
` [P] = [M][v] = [M][LT^(-1)] = [MLT^(-1)]`
(e) Force `[F] = [ma]`
` [F] = [M][a] = [M][LT^(-2)] = [MLT^(-2)]`
(f) `"Work of Energy"= "force" xx "displacement" `
` ["work "] = ["force"] ["displacement"] `
` [MLT^(-2)] [L] = [ML^(2)T^(-2)] `
(g) Power = `("Work")/("Time")`
` ["power"] (["Work "])/(["Time"]) = ([ML^(2)T^(-2)])/([T]) = [.^(2)T^(2)]`
(h) `"Pressure" = ("Force")/("Area")`
` ["Pressure"] = (["Force"])/(["Area"]) = ([MLT^(-2)])/(L^(2))`
` = [ML^(-1)T^(-2) ]`
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