Serial of year 37

On long-term average, how long does it take for the March equinox to move by one day when using the Gregorian calendar?

How much does the period of oscillation of a pendulum with a period of $t=1 \mathrm{s}$ change when its temperature changes by $T=10 \mathrm{\C }$ if its rod and a much heavier weight are made out of copper? What processes affect the pendulum when the atmospheric pressure or air humidity changes?

Estimate how long is the shortest „rod“ from quartz resonating at a frequency $f=5 \mathrm{MHz}$. Consider the density of quartz $\rho =2{,}65 \mathrm{g\cdot cm^{-3}}$ and the modulus of elasticity $E \approx 80 \mathrm{GPa}$ and the compressive oscillations with one static and the other free to move.

Let's have an isotope $\ce {^{a} X}$, that changes with a half-life $T_{1/2}$ to the isotope $\ce {^{b}Y}$. At several places in a sample, we measure the relative isotopic abundance of the parent and child nuclides relative to a different isotope of the child element: $\left [\ce {^{a}X}\right ]/\left [\ce {^{c}Y}\right ]$, $\left [\ce {^{b}Y}\right ]/\left [\ce {^{c}Y}\right ]$. We assume that the relative abundance of the child element does not change in time. How do we determine the age $t$ of the sample? Assume that both isotopes of the element Y are stable and present in original sample and disregard other nuclear transformations.

Measure your elbow in inches. Use only your body parts for the measurement.

In ancient times, the first attempt to determine the distance of the Earth from the Sun was to measure the angular distance of the Moon from the Sun when the Moon was in the first quarter – the interface of light and darkness was direct. Determine the magnitude of this angle and compare it with the angular size of the Earth as seen from the Moon.

State at least $4$ different ways of measuring the velocity of vehicles. Explain which physical principles are used to determine the velocity and which type of velocity it is.

In the diffraction experiment, table salt's grating constant (edge length of the elementary cell) was measured as $563 \mathrm{pm}$. We also know its density as $2{,}16 \mathrm{g\cdot cm^{-3}}$, and that it crystallizes in a face-centered cubic lattice. Determine the value of the atomic mass unit.

A thin rod with a length $l$ and a linear density $\lambda $ lies on a cylinder with a radius $R$ perpendicular to its axis of symmetry. A weight with mass $m$ is placed at each end of the rod so that the rod is horizontal. We carefully increase the mass of one of the weights to $M$. What will be the angle between the rod and the horizontal direction? Assume that the rod does not slide off the cylinder.

Consider a thin-walled glass container of volume $V_1=100 \mathrm{ml}$, the neck of which is a thin and long vertical capillary with internal cross-section $S=0{,}20 \mathrm{cm^2}$, filled with water at temperature $t_1=25 \mathrm{\C }$ up to the bottom of the neck. Now submerge this container in a larger container filled with a volume $V_2=2{,}00 \mathrm{l}$ of olive oil at a temperature $t_2=80 \mathrm{\C }$. How much will the water in the capillary rise?

In a closed container with a volume of $11{,}0 \mathrm{l}$ there is a weak solution containing sodium hydroxide with $p\mathrm {H}=12{,}5$ and a volume of $1{,}0 \mathrm{l}$. In the region above the surface, we burn $100 \mathrm{mg}$ of powdered carbon. Determine the value of the pressure in the container a few seconds after burning out, after half an hour, and after one day. Before the experiment, the vessel contained air of standard composition at standard conditions; similarly, we maintain a standard temperature around the vessel in the laboratory.

Describe three different ways in which the temperature of stars can be determined. What are the basic physical principles they are based on, and what do we need to be careful of?