Final answer:
Correct option: (d) The maximum kinetic energy becomes K1/2.
When the length of a pendulum is doubled, its period increases, leading to a decrease in maximum speed and, hence, its maximum kinetic energy. As the maximum kinetic energy is proportional to the square of the speed, the correct answer is that the maximum kinetic energy becomes K1/2, not 4K1, 2K1, or remaining the same.
Step-by-step explanation:
In a simple harmonic oscillator, the total energy is constant and shared between kinetic energy (K) and potential energy (U), expressed as K + U = constant.
For a pendulum, the maximum kinetic energy is achieved at the lowest point in its swing, where potential energy is at its minimum.
If the length of the pendulum is doubled, the period of the pendulum increases and consequently, the maximum speed of the pendulum decreases, because the period T of a pendulum is given by T = 2π√(L/g), where L is the length and g is the acceleration due to gravity.
Since kinetic energy is given by K = 1/2mv², when the maximum speed decreases, the maximum kinetic energy also decreases.
Therefore, doubling the length of the pendulum will lead to a decrease in the maximum kinetic energy, which rules out options (a) and (b).
Since the gravity and mass of the bob remain unchanged, the total mechanical energy conserved in simple harmonic motion will also remain the same, but not the kinetic energy by itself, which rules out option (c).
The correct answer must be that the maximum kinetic energy becomes K1/2, which is option (d).