JAMB Physics 2023 Paper

Concept:Uniform circular motion requires a centripetal force; the tension in the rope supplies this force.Explanation:Given: $m = 2\,\mathrm{kg}$, $r = 1.2\,\mathrm{m}$, and rotational frequency $f = 120\,\mathrm{rev/min}$.Convert frequency to revolutions per second: $f = \frac{120}{60} = 2\,\mathrm{rev/s}$.Angular velocity is $\omega = 2\pi f = 2\pi \times 2 = 4\pi\,\mathrm{rad/s}$.Centripetal tension is $T = \frac{mv^2}{r}$, where $v = \omega r$.Substituting gives $T = m\omega^2 r$.Insert values: $T = 2 \times (4\pi)^2 \times 1.2$.Calculate: $T = 2 \times 16\pi^2 \times 1.2 = 38.4\pi^2 \approx 379\,\mathrm{N}$.Answer:The tension in the rope is $379\,\mathrm{N}$, which corresponds to option D.