IB Physics HL S2.3 Concluding and Evaluating Questions

A group of students is trying to determine the density and the viscosity of a liquid.

To determine the density, they use a balance to read the mass m of a sphere in air and immersed in the liquid.

They use a sphere of volume $V=1.827 \times 10^{-7} \mathrm{~m}^{3}$.
The readings are $m_{\text {air }}=1.427 \mathrm{~g}$ in air and $m_{\text {immersed }}=1.208 \mathrm{~g}$ in the liquid.
The readings are different due to buoyancy. The buoyancy force $F_{\mathrm{b}}$ is given by

where V is the volume of the sphere and $\rho$ is the density of the liquid.

The students search literature values and find the viscosity of this liquid to be 0.24 , when expressed in SI base units.

Suggest a conclusion reached by the students.

A student attaches one end of a copper wire to an oscillator operating at a fixed frequency. The other end of the wire passes over a pulley to weights that hang vertically. The first harmonic standing wave is established by using the slider to change the length of the wire. The procedure is repeated for different weights.

The mass m of the weights and the wavelength $\lambda$ of the wave are related by

where $\mu$ is a constant, f is the frequency of the wave and $g=9.8 \mathrm{~ms}^{-2}$.

The graph shows the data obtained by the student, plotted to show the variation of m with $\lambda^{2}$.

Suggest a possible reason for the systematic error.

A student investigates whether the Stefan-Boltzmann law, $L=4 \pi \sigma R^{2} T^{4}$, applies to stars.
L= luminosity of the star, in W
$\sigma=$ Stefan-Boltzmann constant
R= radius of the star, in m
T= surface temperature of the star, in K
To verify the law, they obtain values from databases and manipulate the data as shown.

Outline a conclusion for the investigation.