Question

If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
(a) (P – Q)/R
(b) PQ – R
(c) PQ/R
(d) (PR – Q^2)/R
(e) (R + Q)/P

Answer 1

P and Q have different dimensions...  so  P - Q is not proper..

Perhaps  PQ has the same dimensions as that of R.

PQ/R  quantity is alright.

PR could probably have the same dimension as Q^2

R + Q  is not possible... as they have different dimensions.

Answer 2

"The options (a) and (e) can never be meaningful quantities.

According to the law of homogeneity of dimensions, the dimensions of the terms which are either "added or subtracted" must be equal.

It is said that the dimensions of "P, Q, and R" are different. This indicates that Q cannot be subtracted from P and R cannot be added to Q as they are of different dimensions. Thus, options (a) and (e) can never be "meaningful quantities".

It is possible that multiplying the quantities can render equal dimensions that can be either added or subtracted from the other quantities. Thus, it is possible that the options (b), (c) and (d) can be meaningful quantities."