Consider a thin uniform square sheet made of | vedclass

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

Question

(D) For a thin uniform square sheet of side $a$ and mass $m$:$1$. The moment of inertia about an axis passing through the center and perpendicular to

Vedclass · Accepted Answer

$I = \frac{ma^2}{12}$

Vedclass · Answer

(D) For a thin uniform square sheet of side $a$ and mass $m$:$1$. The moment of inertia about an axis passing through the center and perpendicular to the plane of the sheet is $I_z = \frac{ma^2}{6}$.$2$. By the perpendicular axis theorem,$I_z = I_x + I_y$,where $I_x$ and $I_y$ are the moments of inertia about the axes passing through the center and parallel to the sides.$3$. Due to symmetry,$I_x = I_y = \frac{ma^2}{12}$.$4$. Let $I_d$ be the moment of inertia about a diagonal. By the perpendicular axis theorem in the plane of the sheet,if we consider two perpendicular axes along the diagonals,their sum must equal $I_z$.$5$. Since the square is symmetric about both diagonals,the moment of inertia about each diagonal is the same,say $I_d$.$6$. Thus,$I_d + I_d = I_z$,which means $2I_d = \frac{ma^2}{6}$.$7$. Therefore,$I_d = \frac{ma^2}{12}$.

Consider a thin uniform square sheet made of a rigid material. If its side is $a$,mass is $m$,and moment of inertia about one of its diagonals is $I$,then:

Similar Questions

$A$ light ray of wavelength $\lambda$ is passing through a pinhole of diameter $D$ and the effect is observed on a screen placed at a distance $L$ from the pinhole. The approximations of geometrical optics are applicable,if

For a gas,$\frac{R}{C_{V}}=0.4$,where $R$ is the universal gas constant and $C_{V}$ is the molar specific heat at constant volume. The gas is made up of molecules which are

Three moles of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperatures in different states are: $T_1 = 400\, K, T_2 = 800\, K, T_3 = 2400\, K$ and $T_4 = 1200\, K$. The work done by the gas during the cycle is .... $kJ$.

Which of the following values indicates hypertension?

The major product of the reaction is :

Vedclass Test Series

Exam Paper Generator

Online Exam Module