Seven identical coins are rigidly arranged on | vedclass

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

Question

(C) Let $A$ be the centre of the central coin. The moment of inertia of the central coin about an axis through $A$ is $I_{central} = \frac{m r^2}{2}$.

Vedclass · Accepted Answer

$\frac{111}{2}$

Vedclass · Answer

(C) Let $A$ be the centre of the central coin. The moment of inertia of the central coin about an axis through $A$ is $I_{central} = \frac{m r^2}{2}$.For the six surrounding coins,the distance of their centres from $A$ is $2r$. Using the parallel axis theorem,the moment of inertia of each surrounding coin about the axis through $A$ is $I_{surrounding} = \frac{m r^2}{2} + m(2r)^2 = \frac{m r^2}{2} + 4mr^2 = \frac{9}{2} mr^2$.The total moment of inertia of the system about the axis through $A$ is $I_A = I_{central} + 6 	imes I_{surrounding} = \frac{m r^2}{2} + 6 	imes \frac{9}{2} mr^2 = \frac{m r^2}{2} + 27 mr^2 = \frac{55}{2} mr^2$.Now,we need the moment of inertia about point $P$,which is at a distance $d = 2r$ from $A$. Using the parallel axis theorem,$I_P = I_A + M_{total} 	imes d^2$,where $M_{total} = 7m$.$I_P = \frac{55}{2} mr^2 + (7m)(2r)^2 = \frac{55}{2} mr^2 + 28 mr^2 = \frac{55 + 56}{2} mr^2 = \frac{111}{2} mr^2$.

Similar Questions

Consider a uniform square plate of side '$a$' and mass '$m$'. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

The moment of inertia of a rod of length $l$ about an axis passing through its centre of mass and perpendicular to the rod is $I$. The moment of inertia of a hexagonal shape formed by six such rods,about an axis passing through its centre of mass and perpendicular to its plane,will be (in $I$)

About which axis will the moment of inertia of a ring be maximum?

The moment of inertia of a rod of mass $M$ and length $L$ about an axis passing through a point midway between the center and the end is:

For the given square frame $ABCD$ with center $O$,which of the following relations is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module