If P, Q, R are physical quantities, having different dimensions, … - Vidyadip

Question

If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?

$\frac{(\text{P}-\text{Q})}{\text{R}}$
$\text{PQ}-\text{R}$
$\frac{\text{PQ}}{\text{R}}$
$\frac{(\text{PR}-\text{Q}^2)}{\text{R}}$
$\frac{(\text{R}+\text{Q})}{\text{P}}$

✓

Answer

$\frac{(\text{P}-\text{Q})}{\text{R}}$

$\frac{(\text{R}+\text{Q})}{\text{P}}$

Explanation:

In option (a) and (e) there is term (P - Q) and (R + Q) as different physical quantities can never be added or subtracted so option (a) and (e) can never be meaningful.

In option (b), the dimension of PQ may be equal to dimension of R so option (b) can be possible. Similarly dimensions of PR and Q² may be equal and gives the possibility of option (d).

In option (c), there is no addition subtraction gives the possibilities of option (c).

Hence, verifies the right option (a) and (e).

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