IB Physics SL 6.3.3 Units and numerical values Question Bank

A group of students uses pressurized air to move a piston that forces a nail into a block of wood. A gauge is used to measure the pressure P of compressed air above atmospheric pressure. The nail enters the wood perpendicular to its surface.

The students use a ruler to measure the length of the nail which remains above the surface of the wood as shown. The depth of the nail inside the wood is d. All necessary length measurements are recorded using a ruler with uncertainty $\pm 1 \mathrm{~mm}$.

The students suggest the following relationship between d and P :

where k is a constant.
To verify the relationship, the variation of d with $\sqrt{P}$ is plotted.
One data point is missing.

The SI units of k can be expressed as $\mathrm{kg}^{-\frac{1}{2}} \mathrm{~m}^{x} \mathrm{~s}^{y}$. Determine the values of x and y.