T varies inversely as the cube of R. When R = 3, T = \(\frac{2}{81}\), find T when R = 2
- \(\frac{1}{18}\)
-
\(\frac{1}{12}\)
- \(\frac{1}{24}\)
- \(\frac{1}{6}\)
The correct answer is: B
Explanation
T \(\alpha \frac{1}{R^3}\)T = \(\frac{k}{R^3}\)
k = TR3
= \(\frac{2}{81}\) x 33
= \(\frac{2}{81}\) x 27
dividing 81 by 27
k = \(\frac{2}{2}\)
therefore, T = \(\frac{2}{3}\) x \(\frac{1}{R^3}\)
When R = 2
T = \(\frac{2}{3}\) x \(\frac{1}{2^3}\) = \(\frac{2}{3}\) x \(\frac{1}{8}\)
= \(\frac{1}{12}\)
There is an explanation video available .