A circular disc A of radius r is made from an | 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 its central axis is given by $I = \frac{1}{2} M R^2$.Mass $M$ is given by $M = 	ext{Density} 	ime

Vedclass · Accepted Answer

$I_A < I_B$

Vedclass · Answer

(C) The moment of inertia of a circular disc about its central axis is given by $I = \frac{1}{2} M R^2$.Mass $M$ is given by $M = 	ext{Density} 	imes 	ext{Volume} = ho 	imes (\pi R^2 t)$,where $ho$ is the density of iron.For disc $A$:Radius $R_A = r$,thickness $t_A = t$.$M_A = ho \pi r^2 t$.$I_A = \frac{1}{2} M_A R_A^2 = \frac{1}{2} (ho \pi r^2 t) r^2 = \frac{1}{2} ho \pi t r^4$.For disc $B$:Radius $R_B = 4r$,thickness $t_B = t/4$.$M_B = ho \pi (4r)^2 (t/4) = ho \pi (16r^2) (t/4) = 4 ho \pi r^2 t$.$I_B = \frac{1}{2} M_B R_B^2 = \frac{1}{2} (4 ho \pi r^2 t) (4r)^2 = \frac{1}{2} (4 ho \pi r^2 t) (16r^2) = 32 ho \pi t r^4$.Comparing the two:$I_A = 0.5 ho \pi t r^4$$I_B = 32 ho \pi t r^4$Clearly,$I_A < I_B$.

$A$ circular disc $A$ of radius $r$ is made from an iron plate of thickness $t$ and another circular disc $B$ of radius $4r$ is made from an iron plate of thickness $t/4$. The relation between the moments of inertia $I_A$ and $I_B$ is:

Similar Questions

Weights of $1 \ kg$ and $4 \ kg$ are placed at the $20 \ cm$ and $70 \ cm$ marks of a light meter scale,respectively. What is the moment of inertia in $kg \ m^2$ about an axis perpendicular to the scale and passing through the $100 \ cm$ mark?

In a rectangle $ABCD$ where $BC = 2AB$,the moment of inertia will be minimum about which axis?

The moment of inertia of a uniform rectangular plate about an axis passing through its center and parallel to its length $(l)$ is ($b =$ width of the rectangular plate):

Define moment of inertia,write its unit and dimensional formula.

One quarter sector is cut from a uniform circular disc of radius $R$. This sector has mass $M$. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

Vedclass Test Series

Exam Paper Generator

Online Exam Module