Final answer:
Under Jupiter's greater gravitational pull, a pendulum's period will be shorter compared to when under Earth's gravity.
Step-by-step explanation:
When you set a pendulum with a length of 0.5 m and a mass of 1 kg to swing under Jupiter's gravity and measure the time for ten full cycles to calculate the period, you'll find that the period will be shorter compared to Earth's gravity. This is because the period of a simple pendulum depends on the length of the string and the acceleration due to gravity, which is stronger on Jupiter than on Earth. Therefore, the correct answer is (a) The period is shorter compared to Earth's gravity.