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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 Z represent frequency then choose the correct alternative

A

The dimension of X is `[ML^(1) T^(-3)]`

B

The dimension of Y is `[M^(0)LT^(-1)]`

C

The dimension of `beta` is `[M^(0)L^(-1)T^(0)]`

D

The dimension of `alpha` is `[M^(0)L^(1) T^(0)]`

Text Solution

Verified by Experts

The correct Answer is:
B
If `D(Z)=T^(-1)`. Then `D(Y)=?`
from equation (ii) : `D(X)=[T^(-1)ML^(2)T^(-2)]=[ML^(2)T^(-3)]`
So from equation (i) : `D(Y)=(D(X))/(D(F))=[(ML^(2)T^(-3))/(MLT^(-2))]=[LT^(-1)]`
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