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  • A circular platform is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity of <img alt="10 \mathrm{rad} / \mathrm{s}" src

A circular platform is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity of 10 \mathrm{rad} / \mathrm{s}. If by some mechanism, the moment of inertia of the system becomes four times of its initial value. Find the final Kinetic energy of the system, if initial Kinetic energy was 100 Joule.

Option: 1

75 Joule


Option: 2

100 Joule


Option: 3

50 Joule


Option: 4

25 Joule


Answers (1)

best_answer

using conservation of angular momentum

\begin{aligned} & I_1 \omega_1=I_2 \omega_2 \\ & \omega_2=\left(\frac{I_1}{I_2}\right) \omega_1=\frac{\omega_1}{4}=2.5 \mathrm{rad} / \mathrm{s} \\ & K_i =\frac{1}{2} I_1 \omega_1^2, \quad K_f=\frac{1}{2} I_2 \omega_2^2 \\ & \frac{K_i }{K_f}=\left(\frac{I_1}{I_2}\right)\left(\frac{\omega_1}{\omega_2}\right)^2=\left(\frac{1}{4}\right)(4)^2=(4) \\ & K_f=\frac{K_i}{4}=\frac{100}{4}=25 Joule\mathrm{} \end{aligned}

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manish

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