Two discs of same thickness but of different | vedclass

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

Question

(B) The moment of inertia of a disc about its central axis is given by $I = \frac{1}{2}MR^2$.Since mass $M = 	ext{density} (ho) 	imes 	ext{volume

Vedclass · Accepted Answer

$3:1$

Vedclass · Answer

(B) The moment of inertia of a disc about its central axis is given by $I = \frac{1}{2}MR^2$.Since mass $M = 	ext{density} (ho) 	imes 	ext{volume} (V) = ho 	imes (\pi R^2 t)$,where $t$ is the thickness.Given that $M$ and $t$ are the same for both discs,we have $M = ho \pi R^2 t$,which implies $R^2 = \frac{M}{\pi ho t}$.Substituting this into the expression for $I$:$I = \frac{1}{2} M \left( \frac{M}{\pi ho t} ight) = \frac{M^2}{2 \pi t ho}$.Since $M$ and $t$ are constant,$I \propto \frac{1}{ho}$.Therefore,the ratio of the moments of inertia is $\frac{I_1}{I_2} = \frac{ho_2}{ho_1}$.Given $\frac{ho_1}{ho_2} = \frac{1}{3}$,we have $\frac{ho_2}{ho_1} = \frac{3}{1}$.Thus,the ratio of the moments of inertia is $3:1$.

Similar Questions

The moment of inertia of a straight thin rod of mass $M$ and length $l$ about an axis perpendicular to its length and passing through its one end,is

Four point masses each of mass $m$ are placed at the corners of a square $ABCD$ of side length $\ell$. What is the moment of inertia about an axis passing through $A$ and parallel to $BD$?

Two identical thin rods of mass $M \ kg$ and length $L \ m$ are connected as shown in the figure. The moment of inertia of the combined rod system about an axis passing through point $P$ and perpendicular to the plane of the rods is $\frac{x}{12} M L^2 \ kg \ m^2$. The value of $x$ is . . . . . . .

$A$ thin uniform wire of mass $m$ and linear mass density $\rho$ is bent in the form of a circular loop. The moment of inertia of the loop about its diameter is

Three thin uniform rods each of mass $M$ and length $L$ are placed along the three axes of a Cartesian coordinate system with one end of all the rods at the origin. The moment of inertia of the system of the rods about the $z$-axis is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module