Two rods of equal mass m and length l lie along x axis and y axis with their centres at origin

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Two rods equal mass $$m$$ and length $$\ell$$ lie along the $$x$$ axis and $$y$$ axis with their centres origin. What is the moment of inertia of both about the line $$x = y$$ :

• A

  $$\dfrac{m\ell^2}{3}$$

• B

  $$\dfrac{m\ell^2}{4}$$

• C

  $$\dfrac{m\ell^2}{12}$$

• D

  $$\dfrac{m\ell^2}{6}$$

Moment of inertial of a rod of about an axis passing through centre and perpendicular to length :

$$I=\dfrac{M{l}^{2}}{12}$$

moment of inertia of the rod about an axis inclined an angle $$\theta$$ to the original axis:

$${I}^{\prime}=I{\sin}^{2}{\theta}$$

The line $$x=y$$ makes an angle of $${45}^{\circ}$$ about $$x$$ and $$y$$ axes.

Hence $${I}^{\prime}=I{\sin}^{2}{{45}^{\circ}}=\dfrac{I}{2}$$

moment of inertia of both rods about the line passing through $$x=y$$

$${I}_{two/, rods}=2{I}^{\prime}$$

$$=2\times\dfrac{I}{2}=I$$

$$=\dfrac{M{l}^{2}}{12}$$

Two rods of equal length L and equal mass M are kept along x and y axis respectively such that their centres of mass lie at the origin. The moment of inertia about the line y = x, isA. M L2/6D. ML 2/12/ M L 24

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