Uniform square plate of mass $120 g$ is made to rotate about an axis passing through any diagonal of plate. If its moment of inertia is $2 \times 10^{- 2} k g m^{2}$ , then its side length is:

100 c m

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100 m

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120 c m

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120 m

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Solution

The correct option is A $100 c m$
We know that MI about the axis perpendicular to plane passing through center is $I_{z} = m l^{2} / 6$
so using perpendicular theorem , MI about an axis passing through any diagonal of plate $I = I_{z} / 2 = m l^{2} / 12$
So, $\frac{m l^{2}}{12} = 2 \times 10^{- 4}$ , $m = 240 \times 10^{- 3} k g$
we get $l = 0.1 m o r 10 c m$

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Uniform square plate of mass 120 g is made to rotate about an axis passing through any diagonal of plate. If its moment of inertia is 2×10−2kgm2, then its side length is:

The correct option is A 100 cmWe know that MI about the axis perpendicular to plane passing through center is Iz=ml2/6 so using perpendicular theorem , MI about an axis passing through any diagonal of plate I=Iz/2=ml2/12So, ml212=2×10−4 , m=240×10−3kgwe get l=0.1m or 10cm

Uniform square plate of mass $120 g$ is made to rotate about an axis passing through any diagonal of plate. If its moment of inertia is $2 \times 10^{- 2} k g m^{2}$ , then its side length is: