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19 December, 17:22

A mass of 0.450 kg rotates at constant speed with a period of 1.45 s at a radius R of 0.140 m in the apparatus used in this laboratory. What is the rotation period for a mass of 0.550 kg at the same radius

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  1. 19 December, 19:36
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    1.603 s

    Explanation:

    Given that

    Initial mass, = 0.45 kg

    Initial period, = 1.45 s

    Initial radius, = 0.14 m

    Final mass, = 0.55 kg

    Final period, = ?

    Final radios, = 0.14 m

    Since we are finding the rotation period of two masses of same radius, we can assume that the outward force is the same in both cases. This means that

    m₁r₁ω₁² = m₂r₂ω2²

    Where, ω = 2π/T, on substituting, we have

    0.45 * 0.14 * (2π / 1.45) ² = 0.550 * 0.14 * (2π / T₂) ²

    0.45 / 1.45² = 0.550 / T₂²

    T₂² = 0.550 * 1.45² / 0.45

    T₂² = 2.56972

    T₂ = √2.56972

    T₂ = 1.603 sec
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