Question

If L, M, N are physical quantities with different
dimensions, then which of the following
combinations can never be a meaningful quantity?
LM
(1)LM/N
(2) LN-M
(3) (LN-M square)/N
(4) L-M/N​

Answer 1

L-M/N can never be a meaningful quantity.

• L, M and N are of different dimensions.
• Two different dimensions can never be added or subtracted.

a) LM/N

• L and M is multiplied here which is possible.
• N can be divisible also.

b) LN - M

• L and N is multiplied here which is possible.
• It may be LN has same dimension as M.

c) LN-M²/N

• L and N is multiplied here which is possible.
• It may also possible that LN and M² have the same dimension.

d) L-M/N

• It can't be possible as it is mentioned that L and M have different dimensions.

• Two different dimensions can never be added or subtracted.