Physics - Unit & Dimension Question with Solution | TestHub

Solution:

A conversion of units, such as $1\mathrm{m}=100\mathrm{cm}$, expresses the same physical quantity in different units. Both sides of the equality represent a length, so they have identical dimensions (length). The units themselves are different (meters vs. centimeters), but the underlying physical quantity remains unchanged.

Explanation:

Option A is correct. When converting units, the physical quantity itself does not change, only its numerical representation and the unit used. For example, $1\mathrm{m}$ and $100\mathrm{cm}$ both represent the same length. Therefore, both sides of the conversion equation must have the same dimension (e.g., length, mass, time). The units, however, are different.

Option B is incorrect because conversion of units always involves the same dimension on both sides.

Option C is incorrect. If a larger unit is used, the numerical value of the physical quantity will be smaller (e.g., $1\mathrm{m}$ is a larger unit than $1\mathrm{cm}$, and $1$ is smaller than $100$).

Option D is incorrect because the physical quantity being measured does not change during unit conversion; only its expression changes.