Answer
A mass $m=4\text{ gm}$ and velocity $v=6\text{ centimeters per second}$ has a kinetic energy of 72 erg.
Work Step by Step
According to the question, $e\propto m{{v}^{2}}$ which can be written as $e=km{{v}^{2}}$ where $e$ is Kinetic energy, $m$ is the mass, $v$ is the velocity and $k$ is the constant. We have to find the value of constant $k$ for the given data i.e. $m=4,v=6$ and $e=36$.
Substitute the values of e, m, and v in the above formula to find the value of k.
$\begin{align}
& e=km{{v}^{2}} \\
& 36=k\left( 8 \right){{\left( 3 \right)}^{2}} \\
& 36=k\left( 8 \right)\left( 9 \right) \\
& k=\frac{36}{72}
\end{align}$
So,
$\begin{align}
& k=\frac{1}{2} \\
& k=0.5
\end{align}$
Now, calculate the value of e.
$\begin{align}
& e=0.5m{{v}^{2}} \\
& e=0.5\left( 4 \right){{\left( 6 \right)}^{2}}\ \left( \because \ m=4\And v=6 \right) \\
& e=0.5\left( 4 \right)\left( 36 \right) \\
& e=72\text{ergs}
\end{align}$
Therefore, mass $m=4\text{ gms}$ and velocity $v=6\text{ centimetres per second}$ has a kinetic energy of $72\text{ }erg$.
