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A wire forms an angle θ with the vertical while a mass moves at a speed of 10 m/s in a circular path of radius 10 m. If the tension in the wire satisfies T cos θ = mg, determine the value of θ.

1. θ = 30°
2. θ = 45°
3. θ = 60°
4. θ = 90°

Correct answer: θ = 45°

Solution

The condition T cos θ = mg implies that the vertical component of tension balances the weight of the object. This is consistent with θ = 45° when considering the forces in equilibrium.

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