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Question
If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
- (P – Q)/R
- PQ – R
- PQ/R
- (PR – Q2)/R
- (R + Q)/P
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Solution
a. (P – Q)/R
e. (R + Q)/P
Explanation:
Principle of Homogeneity of dimensions: It states that in a correct equation, the dimensions of each term added or subtracted must be the same. Every correct equation must have the same dimensions on both sides of the equation.
According to the problem P, Q and R are having different dimensions, since, the sum and difference of physical dimensions, are meaningless, i.e., (P – Q) and (R + Q) are not meaningful.
So in option (b) and (c), PQ may have the same dimensions as those of R and in options (d) PR and Q2 may have the same dimensions as those of R.
Hence, they cannot be added or subtracted, so we can say that (a) and (e) is not meaningful.
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