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Physical World

Question

The moment of inertia of a body about a given axis 1.2 kgm²_•Initially the body is at rest. In order to produce a rotational kinetic energy of 1500 J and angular acceleration of 25 rad/s² must be applied about the axis for a duration of

10s

8s

2s

4s

Solution

Given:- kinetic energy E=1500J,

E= $\frac{1}{2} {Iω}^{2}$ $\Rightarrow$ $ω^{2} = \frac{2 E}{I}$

$ω^{2} = \frac{2 \times 1500}{1.2} = 2500$

$ω = \sqrt{2500} = 50 rad / \sec t = \frac{ω}{α} = \frac{50}{25} = 2 \sec$