Question

A and B are the numerical values of a physical quantity and C anf D are its units in two systems of measurements. If C>D,then​

Answer 1

Answer:

If C>D, then​ A<B

Explanation:

Now,

Physical quantity = Numerical value * Unit

and

Numerical Value is inversely proportional to unit.

So,

A is inversely proportional to C

B is inversely proportional to D.

So,

A/B = D/C

But since C>D so D/C <1

So, A < B

Answer 2

Answer:

If A and B are 2 numerical values of the same physical quantities with C and D units, then A<B, when C>D.

Explanation:

Given - 2 physical quantities' values = A and B

             2 units = C and D

To find - the relationship between A and B, if C>D

Formula - $Physical\; quantity = Numerical\; Value \times \; Unit$

Solution - We can write the physical quantities as A C and B D.

                  Going by the above mentioned formula, we understand that the numerical value of a physical quantity is inversely proportional to its unit, provided that the physical quantity remains constant.

Thus, $A \propto \frac{1}{C}\\\\B \propto \frac{1}{D}$

We can also write it as $\frac{A}{B} = \frac{D}{C}$

We're given that C>D.

So, we understand that $\frac{D}{C} < 1$

This means, $\frac{A}{B} < 1$

So, we can conclude that A<B.

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