Two discs of same mass and different radii ar | vedclass

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

Question

(C) The moment of inertia of a disc of mass $M$ and radius $R$ about its diameter is given by $I = \frac{1}{4}MR^2$.Since the masses $M_1$ and $M_2$ a

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(C) The moment of inertia of a disc of mass $M$ and radius $R$ about its diameter is given by $I = \frac{1}{4}MR^2$.Since the masses $M_1$ and $M_2$ are equal,the ratio of the moments of inertia is $\frac{I_1}{I_2} = \frac{R_1^2}{R_2^2}$.The mass of a disc is $M = ho \cdot V = ho \cdot \pi R^2 t$,where $ho$ is density and $t$ is thickness.Given $M_1 = M_2$,we have $ho_1 R_1^2 t_1 = ho_2 R_2^2 t_2$.Thus,$\frac{R_1^2}{R_2^2} = \frac{ho_2 t_2}{ho_1 t_1}$.Given $\frac{ho_1}{ho_2} = \frac{3}{5}$,so $\frac{ho_2}{ho_1} = \frac{5}{3}$.Given $t_1 = 1\,cm$ and $t_2 = 0.5\,cm$,so $\frac{t_2}{t_1} = \frac{0.5}{1} = \frac{1}{2}$.Substituting these values,$\frac{R_1^2}{R_2^2} = \frac{5}{3} 	imes \frac{1}{2} = \frac{5}{6}$.Therefore,the ratio of the moments of inertia is $\frac{5}{6}$.Comparing this with $\frac{x}{6}$,we get $x = 5$.

Similar Questions

$A$ solid hemisphere and a hemispherical shell are joined as shown. Both of them have a mass of $m/2$ individually. Find the moment of inertia about the axis $AB$.

The figure shows an isosceles triangular plate of mass $M$ and base $L$. The angle at the apex is $90^o$. The apex lies at the origin and the base is parallel to the $X$-axis. The moment of inertia of the plate about the $y$-axis is:

Two rods of equal mass $m$ and length $l$ lie along the $x$-axis and $y$-axis with their centers at the origin. What is the moment of inertia of both about the line $x=y$?

$A$ wire of mass $M$ and length $L$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is

The ratio of masses and radii of two circular rings are $1 : 2$ and $2 : 1$ respectively. What is the ratio of their moments of inertia about their central axes?

Vedclass Test Series

Exam Paper Generator

Online Exam Module