A vertical string, suspended from a fixed point and having a small mass attached to the free end is set into…

Analyze the question: A simple pendulum swings back and forth. We must decide which of the three statements are true.

Concept: In a simple pendulum, energy continually changes between potential energy (PE) and kinetic energy (KE). If we ignore air resistance and friction at the pivot (the usual assumption in such questions), the total mechanical energy is conserved.

Checking each statement:

• i. PE is a minimum at the middle of the swing. The middle of the swing is the lowest point, where the mass is at its lowest height. Since PE = mgh, and h is smallest here, PE is a minimum. True.

• ii. KE is a maximum at the middle of the swing. At the lowest point, the speed is greatest, because the PE lost has been converted to KE. So KE = ½mv² is a maximum. True.

• iii. The sum of PE and KE is constant throughout the swing. By conservation of mechanical energy (for an ideal pendulum), PE + KE = constant. At the extremes, all the energy is PE (KE = 0). At the middle, it is mostly KE (PE is at its minimum). The total stays the same. True.

All three statements are correct.

Note: In a real pendulum, air resistance would gradually reduce the total energy, but the question is about the ideal system, which is what WASSCE expects.

Answer: A. i, ii and iii

Exam tip: For pendulum questions, remember the pattern:

• Lowest point (middle): KE maximum, PE minimum
• Highest points (ends): KE zero, PE maximum
• Total energy: constant (ignoring friction)

If a statement fits this pattern, it's almost certainly correct.