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Standard XII

Physics

Deducing Mathematically

The moment of...

Question

The moment of inertia of a body about a given axis is $1.2 k g - m^{2}$ . Initially, the body is at rest. In order to produce a rotational $KE$ of $1500 joule$ , an angular acceleration of $25 {rad/sec}^{2}$ must be applied about that axis for the duration of-
(correct answer + 1, wrong answer - 0.25)

4 s

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2 s

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8 s

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10 s

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Solution

The correct option is B $2 s$
As rotational kinetic energy is
$K_{R} = \frac{1}{2} I ω^{2} = \frac{1}{2} I (α t)^{2} = \frac{1}{2} I α^{2} t^{2}$
$1500 = \frac{1}{2} \times 1.2 \times (25)^{2} t^{2}$
or $t^{2} = 4$ or $t = 2 s$

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The moment of inertia of a body about a given axis is 1.2 kg−m2. Initially, the body is at rest. In order to produce a rotational KE of 1500 joule, an angular acceleration of 25 rad/sec2 must be applied about that axis for the duration of- (correct answer + 1, wrong answer - 0.25)

The correct option is B 2 sAs rotational kinetic energy is KR=12Iω2=12I(αt)2=12Iα2t2 1500=12×1.2×(25)2t2 or t2=4 or t=2 s

The correct option is B $2 s$
As rotational kinetic energy is
$K_{R} = \frac{1}{2} I ω^{2} = \frac{1}{2} I (α t)^{2} = \frac{1}{2} I α^{2} t^{2}$
$1500 = \frac{1}{2} \times 1.2 \times (25)^{2} t^{2}$
or $t^{2} = 4$ or $t = 2 s$