ABC is a triangular plate of uniform thicknes | vedclass

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

Question

(C) The moment of inertia $(I)$ of a body depends on the distribution of mass relative to the axis of rotation. The farther the mass is from the axis,

Vedclass · Accepted Answer

$I_{BC} > I_{AB}$

Vedclass · Answer

(C) The moment of inertia $(I)$ of a body depends on the distribution of mass relative to the axis of rotation. The farther the mass is from the axis,the greater the moment of inertia.For a triangular plate,the moment of inertia about an axis is proportional to the square of the distance of the center of mass from that axis.Let the height of the triangle with respect to base $BC$ be $h_A = AB = 4$ units.Let the height of the triangle with respect to base $AB$ be $h_C = BC = 3$ units.Let the height of the triangle with respect to hypotenuse $AC$ be $h_B$. Since the area is $\frac{1}{2} 	imes 3 	imes 4 = 6$,we have $\frac{1}{2} 	imes 5 	imes h_B = 6$,so $h_B = 2.4$ units.The moment of inertia is proportional to the square of the perpendicular distance of the center of mass from the axis. The distance of the centroid from any side is $\frac{1}{3}$ of the altitude to that side.Thus,$I \propto h^2$.$I_{AB} \propto (BC)^2 = 3^2 = 9$$I_{BC} \propto (AB)^2 = 4^2 = 16$$I_{CA} \propto (h_B)^2 = (2.4)^2 = 5.76$Comparing these values,we get $I_{BC} > I_{AB} > I_{CA}$.Therefore,the relation $I_{BC} > I_{AB}$ is correct.

$ABC$ is a triangular plate of uniform thickness. The sides are in the ratio $3:4:5$ as shown in the figure. $I_{AB}, I_{BC}, I_{CA}$ are the moments of inertia of the plate about axes $AB, BC$ and $CA$ respectively. Which one of the following relations is correct?

Similar Questions

$A$ motorcyclist of mass $m$ is to negotiate a curve of radius $r$ with a speed $v$. The minimum value of the coefficient of friction so that this negotiation may take place safely,is

The $pH$ of a buffer solution decreases by $0.02$ units when $0.12 \ g$ of acetic acid is added to $250 \ mL$ of a buffer solution of acetic acid and potassium acetate at $27^{\circ} C$. The buffer capacity of the solution is

For the reaction $A + 2B \rightleftharpoons 2C + D$,the initial concentration of $A$ is $a$ and the initial concentration of $B$ is $1.5$ times that of $A$. If the concentrations of $A$ and $D$ are equal at equilibrium,what will be the concentration of $B$ at equilibrium?

What does a mature sperm contain?

Electric field at a point varies as $r^0$ for

Vedclass Test Series

Exam Paper Generator

Online Exam Module