This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

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9.112 m
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b) Three factors that can increase the strength of a U-shaped soft iron core electromagnet are: • Increasing the current flowing through the coil. • Increasing the number of turns in the coil. • Increasing the cross-sectional area or permeability of the soft iron core.
a) i) To determine the height on a water barometer: Step 1: State the principle that atmospheric pressure is constant. The atmospheric pressure () is the same for both barometers. Step 2: Simplify the equation by canceling . Step 3: Identify the given values. Step 4: Substitute the values and solve for .
ii) A force pump must be used instead of a lift pump to raise water from a deep well over because a lift pump relies on atmospheric pressure, which can only push water up to a maximum height of approximately (at sea level). A force pump, however, can exert a positive pressure to push water to much greater heights, overcoming this atmospheric pressure limit.
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This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.