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

$A$ semi-circular disc has mass $M$ and radius $r$. The moment of inertia about an axis passing through its center and perpendicular to the plane of the disc is:

In the given figure,about which axis will the moment of inertia of the triangular frame be maximum? [Given: $AB < BC < AC$]

$A$ circular disc of radius $10 \ cm$ and thickness $5 \ mm$ has a uniform density of $8 \ g/cc$. Find the moment of inertia of the disc about an axis passing through its center and perpendicular to its plane.

$A$ thin rod of length $L$ and mass $M$ is bent at its midpoint into two halves so that the angle between them is $90^o$. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is

Two rods,each of mass $m$ and length $l$,are joined at their centers to form a cross. What is the moment of inertia of the cross about an axis passing through their common center and perpendicular to the plane of the rods?

Vedclass Test Series

Exam Paper Generator

Online Exam Module