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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Here's the solution:
a) When the magnet spins, the magnetic field lines passing through the coil change continuously. This change in magnetic flux linkage through the coil induces an electromotive force (e.m.f.) across the coil, according to Faraday's Law of Electromagnetic Induction. The voltmeter measures this induced e.m.f., resulting in a reading.
b) Step 1: Identify the given values. Primary voltage, Secondary voltage, Number of turns on the primary coil, turns Number of turns on the secondary coil,
Step 2: Use the transformer equation. The relationship between voltage and the number of turns in a transformer is given by:
Step 3: Substitute the values and solve for . Rearrange the equation to solve for : Rounding to a whole number of turns: The number of turns on the secondary coil is .
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Here's the solution: a) When the magnet spins, the magnetic field lines passing through the coil change continuously.
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.