If \(P\) varies inversely as \(V\) and \(V\) varies directly as \(R 2\) find the relationship between \(P\) and \(R\) given that \(R=7\) when P=2
A. \(P=98 R^{2} \)
B. \(P R^{2}=98\)
C. \(P^{2} R=89\)
D. \(P=1 / 98 R\)
E. \(R 2 / 98\)
Correct Answer: B
Explanation
\begin{aligned}
& P \alpha \frac{1}{V}: V \alpha R^{2}: \\
P=& \frac{k}{V}: V=\lambda R^{2} \\
P=& \frac{k}{\lambda R^{2}} \Rightarrow P=\frac{C}{R^{2}}: \text { where } C=\frac{k}{\lambda} \\ &=P R^{2} \\
P=& 2, R=7 \\=&(2)(7)^{2}=98 \\
\quad \therefore P R^{2}=98
\end{aligned}
