For the given square frame ABCD with center O | vedclass

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

Question

(C) Let the side length of the square be $a$ and its mass be $M$.The moment of inertia of a square frame about an axis passing through its center and

Vedclass · Accepted Answer

$I_{AC} = I_{EF}$

Vedclass · Answer

(C) Let the side length of the square be $a$ and its mass be $M$.The moment of inertia of a square frame about an axis passing through its center and perpendicular to its plane is $I_z = Ma^2$.By the perpendicular axis theorem,$I_z = I_x + I_y$. Since the square is symmetric,$I_x = I_y$,so $I_x = I_y = \frac{1}{2} I_z = \frac{1}{2} Ma^2$.Here,$I_{EF}$ is the moment of inertia about an axis passing through the midpoints of opposite sides,which is equivalent to $I_x$ or $I_y$. Thus,$I_{EF} = \frac{1}{2} Ma^2$.$I_{AC}$ is the moment of inertia about the diagonal $AC$. For a square,the moment of inertia about any axis in its plane passing through the center is the same. Therefore,$I_{AC} = I_{EF} = \frac{1}{2} Ma^2$.

For the given square frame $ABCD$ with center $O$,which of the following relations is correct?

Similar Questions

The moment of inertia of a rod (length $l$,mass $m$) about an axis perpendicular to the length of the rod and passing through a point equidistant from its midpoint and one end is:

$A$ thin wire of length $l$ and uniform linear mass density $\rho$ is bent into a circular loop with centre $O$ and radius $r$ as shown in the figure. The moment of inertia of the loop about the axis $XX'$ is

The moment of inertia of a circular disc of radius $2 \,m$ and mass $1 \,kg$ about an axis $XY$ passing through its center of mass and perpendicular to the plane of the disc is $2 \,kg \,m^2$. The moment of inertia about an axis parallel to the axis $XY$ and passing through the edge of the disc is

The moment of inertia of a semicircular ring of radius $R$ and mass $M$ about an axis passing through point $A$ (one end of the ring) and perpendicular to the plane of the paper is:

For a uniform rectangular sheet shown in the figure,the ratio of moments of inertia about the axes perpendicular to the sheet and passing through $O$ (the centre of mass) and $O'$ (corner point) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module