Two discs A and B each of radius r and mass m | vedclass

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

Question

(D) The moment of inertia of a disc of mass $m$ and radius $r$ about an axis passing through its center and perpendicular to its plane is $I_{cm} = \f

Vedclass · Accepted Answer

$5 m r^2$

Vedclass · Answer

(D) The moment of inertia of a disc of mass $m$ and radius $r$ about an axis passing through its center and perpendicular to its plane is $I_{cm} = \frac{1}{2} m r^2$.For disc $A$,the axis passes through its center,so its moment of inertia is $I_A = \frac{1}{2} m r^2$.For disc $B$,the axis is at a distance $d = 2r$ from its center. Using the parallel axis theorem,$I_B = I_{cm} + m d^2 = \frac{1}{2} m r^2 + m(2r)^2 = \frac{1}{2} m r^2 + 4 m r^2 = \frac{9}{2} m r^2$.The total moment of inertia of the system is $I_{total} = I_A + I_B = \frac{1}{2} m r^2 + \frac{9}{2} m r^2 = \frac{10}{2} m r^2 = 5 m r^2$.

Two discs $A$ and $B$ each of radius $r$ and mass $m$ are attached as shown to form a system. The moment of inertia of this system about an axis perpendicular to the plane of the discs and passing through the center of disc $A$ is

Similar Questions

The moment of inertia of a sphere about its diameter is $40 \ kg \cdot m^2$. Find the moment of inertia about any tangent.

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about its tangent is:

$A$ thin metal wire of length $L$ and uniform linear mass density $Q$ is bent into a circular coil with $O$ as the center. The moment of inertia of the coil about the axis $XX'$ is:

$A$ solid sphere of radius $R$ has mass $M$. The moment of inertia of the solid sphere about an axis at a distance $\frac{R}{2}$ from the centre is:

Moment of inertia of a disc of mass $M$ and radius $R$ about any of its diameter is $MR^2/4$. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be $(x/2)MR^2$. The value of $x$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module