Four spheres of diameter 2a and mass M are pl | vedclass

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

Question

(B) Let the axis of rotation be along the side connecting the centers of spheres $A$ and $B$.$1$. For spheres $A$ and $B$,the axis of rotation passes

Vedclass · Accepted Answer

$\frac{8}{5}Ma^2 + 2Mb^2$

Vedclass · Answer

(B) Let the axis of rotation be along the side connecting the centers of spheres $A$ and $B$.$1$. For spheres $A$ and $B$,the axis of rotation passes through their centers. The moment of inertia of a solid sphere about its diameter is $I_{cm} = \frac{2}{5}Ma^2$. Thus,$I_A = I_B = \frac{2}{5}Ma^2$.$2$. For spheres $C$ and $D$,the axis of rotation is at a perpendicular distance $b$ from their centers. Using the parallel axis theorem,$I = I_{cm} + Md^2$,where $d = b$. Thus,$I_C = I_D = \frac{2}{5}Ma^2 + Mb^2$.$3$. The total moment of inertia of the system is $I_{total} = I_A + I_B + I_C + I_D$.$I_{total} = \frac{2}{5}Ma^2 + \frac{2}{5}Ma^2 + (\frac{2}{5}Ma^2 + Mb^2) + (\frac{2}{5}Ma^2 + Mb^2) = \frac{8}{5}Ma^2 + 2Mb^2$.

Four spheres of diameter $2a$ and mass $M$ are placed with their centers on the four corners of a square of side $b$. The moment of inertia of the system about an axis along one of the sides of the square is

Similar Questions

$A$ wire of mass $m$ and length $l$ is bent in the form of a circular ring. The moment of inertia of the ring about its axis is:

The moment of inertia of a uniform thin rod of length $L$ and mass $M$ about an axis passing through a point at a distance of $\frac{L}{3}$ from one of its ends and perpendicular to the rod is

Four particles each of mass $M$ are placed at the corners of a square of side $L$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

Four identical point masses (each of mass $m$) are placed on the circumference of a disc. The disc has mass $M$ and radius $R$. What will be the moment of inertia about an axis passing through the center $O$ and perpendicular to the plane of the disc?

Four solids are shown in cross-section. The sections have equal heights and equal maximum widths. They have the same mass. The one which has the largest rotational inertia about a perpendicular axis through the centre of mass is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module