Physics

Problem

A radioactive substance has mass

m(t)

measured in grams and obeys the differential equation

\dfrac{dm}{dt}=k m^{3}

. If time is measured in seconds, which of the following units must

k

have so that the equation is dimensionally consistent? a)

\text{g}^{2}\,/\,\text{s}

\text{g}\,/\,\text{s}

\text{g}^{-2}\,\text{s}^{-1}

\text{s}^{-1}