Two circular discs A and B are of equal masse | vedclass

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

Question

(C) The moment of inertia of a circular disc about an axis passing through its centre and normal to its circular face is given by $I = \frac{1}{2}MR^2

Vedclass · Accepted Answer

${I_A} < {I_B}$

Vedclass · Answer

(C) The moment of inertia of a circular disc about an axis passing through its centre and normal to its circular face is given by $I = \frac{1}{2}MR^2$.Since the mass $M$ of the disc is given by $M = V\rho = \pi R^2 t \rho$,where $t$ is the thickness and $\rho$ is the density,we can write $R^2 = \frac{M}{\pi t \rho}$.Substituting this into the expression for $I$,we get $I = \frac{1}{2} M \left( \frac{M}{\pi t \rho} \right) = \frac{M^2}{2 \pi t \rho}$.Given that the mass $M$ and thickness $t$ are constant for both discs,we have $I \propto \frac{1}{\rho}$.Therefore,$\frac{I_A}{I_B} = \frac{d_B}{d_A}$.Since it is given that $d_A > d_B$,it follows that $I_A < I_B$.

Two circular discs $A$ and $B$ are of equal masses and thickness but made of metals with densities ${d_A}$ and ${d_B}$ $({d_A} > {d_B})$. If their moments of inertia about an axis passing through their centres and normal to the circular faces are ${I_A}$ and ${I_B}$ respectively,then:

Similar Questions

The ratio of the masses of two circular rings is $1:2$ and the ratio of their diameters is $2:1$. The ratio of their moments of inertia is:

The radius of gyration of a body depends upon:

$A$ uniform square plate $S$ (side $c$) and a uniform rectangular plate $R$ (sides $b$,$a$) $(a > b)$ have identical areas and masses. Based on the figure,which of the following is correct?
$(a)\ I_{xR}/I_{xS} < 1$
$(b)\ I_{yR}/I_{yS} > 1$
$(c)\ I_{zR}/I_{zS} > 1$

On account of the melting of ice at the North Pole,the moment of inertia of the spinning Earth:

Shown in the figure is a hollow ice cream cone (it is open at the top). If its mass is $M$,radius of its top is $R$,and height is $H$,then its moment of inertia about its axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module