K A Tsokos Solutions for Chapter: Measurement and Uncertainties, Exercise 2: Test yourself

The centripetal force is given by $F =\frac{m{v}^2}{r}$. The mass is measured to be $2.8\pm 0.1kg$, the velocity $14\pm 2 m/s$ and the radius $8.0\pm 0.2 m$; find the force on the mass, including the uncertainty.

The radius r of a circle is measured to be $2.4cm\pm 0.1cm$. Find the uncertainty in the area of the circle.

The radius r of a circle is measured to be $2.4cm\pm 0.1cm$. Find the uncertainty in circumference of the circle.

The side of a rectangle are measured as $4.4\pm 0.2 cm$and $8.5\pm 0.3 cm$. Find the area and perimeter of the rectangle.

The length $L$ of a pendulum is increased by $2\%$. Find the percentage increase in the period $T.$

The volume of the cone of base radius $R$and height $h$is given by $V=\frac{{\mathrm{\pi R}}^2\mathrm{h}}{3}$. The uncertainty in the radius and in the height  $4\%$. Find the percentage uncertainty in the volume.

In an experiment to measure current and voltage across a device, the following data was collected

$(V,I) = \left\{\right(0.1,26),)(0.2,48),(0.3,65),(0.4,90)\}$.

The current was measured in $mA$And the voltage in $mV$. The uncertainty in the current was $\pm 4mA$. Plot the current versus the voltage and draw the best-fit line through the points. Suggest whether the current is proportional to the voltage.

The following data was collected for current and voltage

$(V,I) = \left\{\right(0.1,27),(0.2,44),(0.3,60),(0.4,78\left)\right\}$

With uncertainty of $\pm 4mA$in the current. Plot the current versus the voltage and draw the best-fit line. Suggest whether the current is proportional to the voltage.