Answer
$72\;ergs $.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let kinetic energy is $E$,
the mass is $M$,
and velocity is $V$.
$\Rightarrow E=kMV^2$ ...... (1)
Step 2:- Substitute the first set of values into the equation to find the value of $k$.
The given values are $M=8\; grams,V=3\; centimeters\; per \; second$
and $E=36\; ergs$.
Substitute into the equation (1).
$\Rightarrow 36=k(8)(3)^2$
Simplify.
$\Rightarrow 36=72k$
Divide both sides by $72$.
$\Rightarrow \frac{36}{72}=\frac{72k}{72}$
Simplify.
$\Rightarrow 0.5=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=0.5$ into the equation (1).
$\Rightarrow E=0.5MV^2$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $M=4\; grams$ and $V=6\; centimeters\;per\;seconds$ into the equation (2).
$\Rightarrow E=0.5(4)(6)^2$
Simplify.
$\Rightarrow E=72$
Hence, the kinetic energy is $72\;ergs $.
