Three point masses,each of mass m,are placed | vedclass

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

Question

(C) Let the vertices of the equilateral triangle be $A, B,$ and $C$. Let the axis of rotation be along the side $BC$.The masses at $B$ and $C$ lie on

Vedclass · Accepted Answer

$\frac{3}{4} m \ell^{2}$

Vedclass · Answer

(C) Let the vertices of the equilateral triangle be $A, B,$ and $C$. Let the axis of rotation be along the side $BC$.The masses at $B$ and $C$ lie on the axis of rotation,so their perpendicular distance from the axis is $0$. Thus,their moment of inertia is $I_{B} = m(0)^{2} = 0$ and $I_{C} = m(0)^{2} = 0$.The mass at $A$ is at a perpendicular distance $h$ from the side $BC$. In an equilateral triangle of side $\ell$,the height $h$ is given by $h = \ell \sin(60^{\circ}) = \frac{\sqrt{3}}{2} \ell$.The moment of inertia of the mass at $A$ about the axis $BC$ is $I_{A} = m h^{2} = m \left( \frac{\sqrt{3}}{2} \ell \right)^{2} = m \left( \frac{3}{4} \ell^{2} \right) = \frac{3}{4} m \ell^{2}$.The total moment of inertia of the system is $I = I_{A} + I_{B} + I_{C} = \frac{3}{4} m \ell^{2} + 0 + 0 = \frac{3}{4} m \ell^{2}$.

Three point masses,each of mass $m$,are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis along any one side of the triangle is:

Similar Questions

Two rings of same mass $M$ and radius $R$ are placed such that their centers coincide and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the center and perpendicular to any one ring is

Three point masses $m$ are placed at the corners of an equilateral triangle of side length $\ell$. What is the moment of inertia of the system about an axis passing through one side of the triangle?

The given figure shows a disc of mass $M$ and radius $R$ lying in the $x-y$ plane with its center on the $x$-axis at a distance $a$ from the origin. Then,the moment of inertia of the disc about the $x$-axis is:

Two circular discs $A$ and $B$ are of equal masses and thickness but made of metals with densities ${d_A}$ and ${d_B}$ $({d_A} > {d_B})$. If their moments of inertia about an axis passing through their centres and normal to the circular faces are ${I_A}$ and ${I_B}$ respectively,then:

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module