Question

$T$ varies directly as the square of $r$ and inversely as the cube of $s$. If $r$ is tripled and $s$ is doubled, the value of $T$ is

• A. multiplied by $\frac{3}{2}$
• B. multiplied by $6$
• C. multiplied by $\frac{9}{8}$
• D. multiplied by $2$
• E. divided by $2$

Answer 1

Answer: (C)

multiplied by $\frac{9}{8}$

Given that $T\propto \frac{r^2}{s^3}$
Now $r$ is tripled and $s$ is doubled
Therefore, we get $T\propto \frac{{\left(3r\right)}^2}{{\left(2s\right)}^3}\propto \frac{9r^2}{{8s}^3}$
Therefore, the new $T$ will be $\frac{9}{8}$ times the old $T$.