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Question

The moment of inertia of a body about a given axis is $$ 1.2  kg m^{2}$$. Initially the body is at rest. In order to produce a rotational KE of $$1500  J$$, an angular acceleration of $$25  rad /sec^{2}$$ must be applied about that axis for a duration of:


A
4 s
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B
2 s
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C
8 s
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D
10 s
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Solution

The correct option is D 2 s

$$I=1.2\ kgm^2$$

$$\alpha =25\ rad/s^2$$

$$KE = \dfrac{1}{2} I {\omega}^2$$

$$1500 = \dfrac{1}{2}\times 1.2\times {\omega}^2$$

$$50 rad/s = \omega$$

$$\alpha =25\ rad/s^2$$

$$\omega=0+\alpha t$$


$$\dfrac{50}{25}=t=2\ sec$$ 


Physics

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