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A physical quantity X depends on another...

A physical quantity X depends on another physical quantities as `X=YFe^(-beta r^(2))+ZW sin (alpha r)` where r, F and W represents distance, force and work respectively & Y and Z are unknown physical quantities and `alpha, beta` are positive contsnats.
If Y respresent displacement then `dim((alphaYZ)/(betaF))` is equal to

A

`M^(-1) LT^(2)`

B

`M^(-1) L^(2)T^(-2)`

C

`M^(1) L^(1) T^(-2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given `" "X=Yfe^(-betar^(2))+ZW sin (alphar) " "` Here `Dim (beta)=L^(-2), Dim (alpha)=L^(-1)`
Also `" " Dim (X)=Dim(YE)` …(i) & `" "Dim (X)=Dim(ZW)` …(ii)
Now If `" " Dim (Y)=L`
So `" " Dim(X)=[LMLT^(-2)]=[ML^(2)T^(-2)]" "` from equation (i)
and `" " Dim(Z)=Dim(X/W)=[(ML^(2)T^(-2))/(ML^(2)T^(-2))]=[M^(0)L^(0)T^(0)]" "` from equation (ii)
Thus`" "Dim((alphaYZ)/(betaF))=[(L^(-1)L)/(L^(-2)MLT^(-2))]=[M^(-1)LT^(2)]`
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