Physics HSC practice questions

Light of wavelength $350\,\text{nm}$ shines on a metal surface with work function $\phi = 2.0\,\text{eV}$. Determine the stopping potential required to halt the emitted electrons. Use $h = 6.63\times10^{-34}\,\text{J s}$ and $c = 3.00\times10^{8}\,\text{m s}^{-1}$.

Monochromatic light of wavelength $500\,\text{nm}$ illuminates a double‑slit apparatus. The slits are separated by $d = 0.25\,\text{mm}$ and the screen is $L = 2.0\,\text{m}$ from the slits. (a) Derive the formula for the fringe spacing $y$ on the screen. (b) Calculate the distance between the central bright fringe and the fifth-order bright fringe. (c) Discuss two factors that could reduce the visibility of the interference pattern.

A single circular loop of radius $0.10\,\text{m}$ carries a current of $5\,\text{A}$. Using $\mu_0 = 4\pi\times10^{-7}\,\text{T m A}^{-1}$, calculate the magnetic field at the centre of the loop.

Monochromatic light of wavelength $600\,\text{nm}$ passes through a single slit $0.30\,\text{mm}$ wide. Calculate the angular position of the first diffraction minimum.

A particle starts from rest and moves along a straight line with an acceleration that increases linearly with time, $a(t) = k t$, where $k$ is a constant. (a) Derive an expression for the distance $s$ travelled after a time $t$ in terms of $k$. (b) If $k = 2\,\text{m s}^{-3}$, calculate the distance after $5\,\text{s}$. (c) Discuss how the motion would differ if the acceleration were constant instead of variable.

A capacitor of capacitance $C = 100\,\mu\text{F}$ is initially charged to $V_{0}=12\,\text{V}$ and then allowed to discharge through a resistor $R = 2\,\text{k}\Omega$. (a) Derive the expression for the voltage $V(t)$ across the capacitor as a function of time. (b) Calculate the time constant $\tau$ for this circuit. (c) Determine the voltage after a time equal to $3\tau$. (d) Briefly explain why the voltage never reaches zero in theory.

A stone is thrown with an initial speed of $30\,\text{m s}^{-1}$ at an angle of $45^{\circ}$ above the horizontal. Neglect air resistance. Calculate the maximum height reached by the stone. Use $g = 9.8\,\text{m s}^{-2}$.

A car of mass $1500\,\text{kg}$ rounds a flat curve of radius $50\,\text{m}$ at a speed of $20\,\text{m s}^{-1}$. Determine the magnitude of the required centripetal force.

A metal rod $0.50\,\text{m}$ long moves at $3\,\text{m s}^{-1}$ perpendicular to a uniform magnetic field of $0.2\,\text{T}$. Find the magnitude of the induced emf across the ends of the rod.

Compare the Bohr model of the hydrogen atom with the modern quantum mechanical model. (a) List two key postulates of the Bohr model. (b) Explain one major limitation of the Bohr model that the quantum mechanical model overcomes. (c) Describe how the quantum mechanical model accounts for the observed line spectra of hydrogen.