Seven identical discs each of mass M and radi | vedclass

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

Question

(D) The moment of inertia $(I)$ of a single circular disc about an axis passing through its center and perpendicular to its plane is $I_{cm} = \frac{M

Vedclass · Accepted Answer

$\frac{55}{2} MR^2$

Vedclass · Answer

(D) The moment of inertia $(I)$ of a single circular disc about an axis passing through its center and perpendicular to its plane is $I_{cm} = \frac{MR^2}{2}$.For the system of seven discs,the total moment of inertia about the axis passing through the center of the central disc (point $O$) and normal to the plane is the sum of the moment of inertia of the central disc and the six surrounding discs.$1$. For the central disc: The axis passes through its center,so its moment of inertia is $I_1 = \frac{MR^2}{2}$.$2$. For the six surrounding discs: The distance between the center of the central disc and the center of any surrounding disc is $d = 2R$. Using the parallel axis theorem,the moment of inertia of each surrounding disc about the central axis is $I_2 = I_{cm} + Md^2 = \frac{MR^2}{2} + M(2R)^2 = \frac{MR^2}{2} + 4MR^2 = \frac{9MR^2}{2}$.Since there are six such surrounding discs,their total moment of inertia is $6 	imes I_2 = 6 	imes \frac{9MR^2}{2} = 27MR^2$.Total moment of inertia $I = I_1 + 6I_2 = \frac{MR^2}{2} + 27MR^2 = \frac{MR^2 + 54MR^2}{2} = \frac{55MR^2}{2}$.

Similar Questions

Three rods each of mass $m$ and length $L$ are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

$A$ square lamina of side $b$ has the same mass as a disc of radius $R$. The moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $\frac{b}{R}$ is

If a solid sphere of mass $5 \, kg$ and a disc of mass $4 \, kg$ have the same radius $R$,then the ratio of the moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent is $\frac{x}{7}$. The value of $x$ is $.........$

The figure shows a uniform solid block of mass $M$ and edge lengths $a, b,$ and $c$. Its moment of inertia $(M.I.)$ about an axis passing through one edge and perpendicular to the large face of the block (as shown) is:

The moment of inertia of a solid sphere,about an axis parallel to its diameter and at a distance of $x$ from it,is $I(x)$. Which one of the graphs represents the variation of $I(x)$ with $x$ correctly?

Vedclass Test Series

Exam Paper Generator

Online Exam Module