The figure shows a thin metallic triangular s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Consider a square plate of side $l$ and mass $2M$ formed by joining two such triangular sheets $ABC$ along the hypotenuse $AC.$Let the square be $

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Consider a square plate of side $l$ and mass $2M$ formed by joining two such triangular sheets $ABC$ along the hypotenuse $AC.$Let the square be $PQRS$ where $AC$ is a diagonal.The moment of inertia of a square plate of mass $M_{total} = 2M$ and side $l$ about its diagonal is given by $I_{diagonal} = \frac{1}{12} M_{total} l^2.$Substituting $M_{total} = 2M$,we get $I_{diagonal} = \frac{1}{12} (2M) l^2 = \frac{Ml^2}{6}.$Since the square is composed of two identical triangular sheets $ABC$ of mass $M$ each,the moment of inertia of one triangular sheet about the diagonal $AC$ is half of the moment of inertia of the square about the diagonal.Therefore,$I_{AC} = \frac{1}{2} 	imes I_{diagonal} = \frac{1}{2} 	imes \frac{Ml^2}{6} = \frac{Ml^2}{12}.$

The figure shows a thin metallic triangular sheet $ABC.$ The mass of the sheet is $M.$ The moment of inertia of the sheet about side $AC$ is

Similar Questions

Two rings of radius $R$ and $nR$ having different masses and made up of the same wire have the ratio of moment of inertia about an axis passing through the centre as $1 : 8$. The value of $n$ is

The moment of inertia of a solid disc made of thin metal of radius $R$ and mass $M$ about one of its diameters is given by $\frac{M R^2}{4}$. What will be the moment of inertia about this axis,if the disc is folded in half about this diameter?

Three thin uniform rods,each of mass $M$ and length $L$,are placed along the three Cartesian axes such that one end of each rod is at the origin. Find the moment of inertia of this system about the $z$-axis.

The ratio of the radii of gyration of a circular disc to that of a circular ring,each of same mass and radius,around their respective axes is

Vedclass Test Series

Exam Paper Generator

Online Exam Module