In the triangular sheet shown,PQ = QR = l. If | vedclass

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(B) The triangular sheet is a right-angled isosceles triangle with legs of length $l$. The area of the triangle is $A = \frac{1}{2} l^2$.Let the mass

Vedclass · Accepted Answer

$\frac{Ml^2}{12}$

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(B) The triangular sheet is a right-angled isosceles triangle with legs of length $l$. The area of the triangle is $A = \frac{1}{2} l^2$.Let the mass per unit area be $\sigma = \frac{M}{A} = \frac{2M}{l^2}$.The moment of inertia of a thin triangular plate about an axis passing through one of its sides of length $b$ and height $h$ is given by $I = \frac{Mh^2}{6}$.In this case,for the axis $PR$,the base is the hypotenuse $PR = \sqrt{l^2 + l^2} = l\sqrt{2}$.The height $h$ of the triangle from vertex $Q$ to the hypotenuse $PR$ is $h = \frac{l}{\sqrt{2}}$.Substituting these values into the formula $I = \frac{Mh^2}{6}$:$I = \frac{M (l/\sqrt{2})^2}{6} = \frac{M (l^2/2)}{6} = \frac{Ml^2}{12}$.

In the triangular sheet shown,$PQ = QR = l$. If $M$ is the mass of the sheet,what is the moment of inertia about the axis $PR$?

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