Topic: Other
Concepts: Dimensional analysis

Solution:

• A) The dimension of $g$ is $L/T^2$. Since you don’t have any tools to measure length in SI units, you can’t measure $g$ in SI units.
• B) The dimension of $c$ is $L/T$. Since you don’t have any tools to measure length in SI units, you can’t measure $c$ in SI units.
• C) The dimension of $\rho$ is $M/L^3$. Since you don’t have any tools to measure length in SI units, you can’t measure $\rho$ in SI units.
• D) The dimension of $k$ is $M/T^2$. Since your mass and tuning fork can measure mass and time in SI units, you can measure $k$ in SI units.
• E) The dimension of $P$ is $M/LT^2$. Since you don’t have any tools to measure length in SI units, you can’t measure $P$ in SI units.

Thus, the answer is D.