Four particles,each of mass M,are placed at t | vedclass

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

Question

(D) The moment of inertia $I$ of a system of particles about an axis is given by $I = \sum m_i r_i^2$,where $r_i$ is the perpendicular distance of the

Vedclass · Accepted Answer

$\frac{L}{\sqrt{2}}$

Vedclass · Answer

(D) The moment of inertia $I$ of a system of particles about an axis is given by $I = \sum m_i r_i^2$,where $r_i$ is the perpendicular distance of the $i$-th particle from the axis.For a square of side $L$,the distance of each corner from the centre is $r = \frac{	ext{diagonal}}{2} = \frac{\sqrt{2}L}{2} = \frac{L}{\sqrt{2}}$.Since there are four particles each of mass $M$,the total moment of inertia $I$ about the axis passing through the centre and perpendicular to the plane is:$I = 4 	imes M 	imes r^2 = 4 	imes M 	imes (\frac{L}{\sqrt{2}})^2 = 4 	imes M 	imes \frac{L^2}{2} = 2ML^2$.The radius of gyration $k$ is defined by the relation $I = Mk_{total} k^2$,where $M_{total} = 4M$.So,$2ML^2 = (4M)k^2$.$k^2 = \frac{2ML^2}{4M} = \frac{L^2}{2}$.$k = \frac{L}{\sqrt{2}}$.

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:

Similar Questions

$A$ uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A$. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $\frac{ml^2}{3}$,the initial angular acceleration of the rod will be:

Which of the following compounds contains an $S - S$ bond?

$A$ conducting rod of length $\ell$ is moving with velocity $v$ in a uniform magnetic field $B$ directed into the plane of the paper,as shown in the diagram. Which end of the rod is at a lower potential?

The monomer $( X )$ involved in the synthesis of Nylon $6,6$ gives positive carbylamine test. If $10$ moles of $X$ are analyzed using Dumas method, the amount $($in grams$)$ of nitrogen gas evolved is $....$
Use: Atomic mass of $N ($in amu$) = 14$

$A$ torch bulb rated as $4.5\, W, 1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ............. $V$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module