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When a pendulum clock is moved to a hill station at an altitude `h` above sea level, the correct adjustment required to keep the correct time is to reduce the length of the pendulum (option 1).
The time it takes for a pendulum to swing back and forth (also known as its period) is determined by the length of the pendulum. When the clock is moved to a higher altitude, the gravitational force acting on the pendulum decreases slightly. As a result, the pendulum will swing more quickly and the clock will run faster.
To compensate for this increase in speed, the length of the pendulum needs to be reduced. By reducing the length, the period of the pendulum increases, causing it to swing more slowly and keeping the clock`s time accurate.
It is important to note that the mass of the pendulum (option 3) or the mass of the clock (option 4) does not affect the timekeeping accuracy in this situation. The adjustment required is solely related to the length of the pendulum.