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

Two solid spheres ($A$ and $B$) are made of metals of different densities $\rho_A$ and $\rho_B$ respectively. If their masses are equal, the ratio of their moments of inertia $(I_B / I_A)$ about their respective diameter is

Obtain the expression for the moment of inertia and define it. What are the factors on which the moment of inertia depends? Write its unit and dimensional formula.

The moment of inertia of a circular wire of mass $M$ and radius $R$ about its diameter is .......

If a person sitting on a rotating stool with his hands outstretched, suddenly lowers his hands, then his

$A$ flywheel is constructed such that its entire mass is concentrated at the rim because:

Vedclass Test Series

Exam Paper Generator

Online Exam Module