As shown in the figure,two thin coplanar circ | vedclass

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

Question

(D) The moment of inertia of the system is the sum of the moments of inertia of the two discs about the given axis.Let $I_B$ be the moment of inertia

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(D) The moment of inertia of the system is the sum of the moments of inertia of the two discs about the given axis.Let $I_B$ be the moment of inertia of disc $B$ about an axis perpendicular to its plane and passing through its centre. $I_B = \frac{1}{2} Mr^2$.Let $I_A$ be the moment of inertia of disc $A$ about the same axis. Since the axis is parallel to the axis passing through the centre of disc $A$ at a distance $d = 2r$,we use the parallel axis theorem: $I_A = I_{cm} + Md^2$.Here,$I_{cm} = \frac{1}{2} Mr^2$ and $d = 2r$.So,$I_A = \frac{1}{2} Mr^2 + M(2r)^2 = \frac{1}{2} Mr^2 + 4Mr^2 = 4.5 Mr^2$.The total moment of inertia $I = I_B + I_A = 0.5 Mr^2 + 4.5 Mr^2 = 5 Mr^2$.

As shown in the figure,two thin coplanar circular discs $A$ and $B$ each of mass $M$ and radius $r$ are attached to form a rigid body. The moment of inertia of this system about an axis perpendicular to the plane of disc $B$ and passing through its centre is (in $Mr^2$)

Similar Questions

The radius of gyration $K$ of a hollow sphere of mass $M$ and radius $R$ about an axis $XY$ is equal to $R$. The distance of that axis from the center of the sphere is $h$. The value of $h$ is

For the given uniform square lamina $ABCD$,whose centre is $O$,

Moment of inertia of a disc about its own axis is $I$. Its moment of inertia about a tangential axis in its plane is

Find the moment of inertia of the ring shown in the figure about the axis $AB$.

The moment of inertia of a semicircular ring of radius $R$ and mass $M$ about an axis passing through point $A$ (one end of the ring) and perpendicular to the plane of the paper is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module