JAMB Mathematics 2015 Paper

Concept:Since extension $E$ is directly proportional to tension $T$, we use the linear relation $E = kT$, where $k$ is the constant of proportionality.Explanation:Let the extension be $E$ and the tension be $T$.Given that $E \propto T$, we write $E = kT$.When $T = 8\,\mathrm{N}$, the extension is $E = 2\,\mathrm{cm}$.Substitute these values into $E = kT$:$$2 = k \times 8$$Solve for $k$:$$k = \frac{2}{8} = 0.25$$So the relationship is $E = 0.25T$.Now find $E$ when $T = 12\,\mathrm{N}$:$$E = 0.25 \times 12 = 3\,\mathrm{cm}$$Answer:The extension produced by a tension of $12\,\mathrm{N}$ is $3\,\mathrm{cm}$, which is option D.