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 $C$. The masses are placed at $A, B,$ and $C$. The axis of rotation passes through sid

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Let the vertices of the equilateral triangle be $A, B,$ and $C$. The masses are placed at $A, B,$ and $C$. The axis of rotation passes through side $AB$.$1$. The perpendicular distance of mass at $A$ from the axis $AB$ is $r_A = 0$.$2$. The perpendicular distance of mass at $B$ from the axis $AB$ is $r_B = 0$.$3$. The perpendicular distance of mass at $C$ from the axis $AB$ is the altitude $x$ of the equilateral triangle.Using the Pythagorean theorem in the triangle formed by the altitude:$x^2 + (a/2)^2 = a^2$$x^2 = a^2 - a^2/4 = 3a^2/4$$x = \frac{\sqrt{3}}{2}a$The moment of inertia $I$ of the system about the axis $AB$ is given by:$I = \sum m_i r_i^2 = m(r_A^2) + m(r_B^2) + m(r_C^2)$$I = m(0)^2 + m(0)^2 + m(x)^2$$I = m \left( \frac{\sqrt{3}}{2}a \right)^2 = m \left( \frac{3}{4}a^2 \right) = \frac{3}{4}m a^2$

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

Similar Questions

Assertion $(A)$: The moment of inertia of a steel sphere is larger than the moment of inertia of a wooden sphere of the same radius.
Reason $(R)$: Moment of inertia is independent of the mass of the body.
The correct one is:

Obtain the expression for the moment of inertia and define it. What are the factors on which the moment of inertia depends? Write its unit and dimensional formula.

The moment of inertia of a rigid body about an axis

The moment of inertia of a straight thin rod of mass $M$ and length $l$ about an axis perpendicular to its length and passing through its one end,is

Vedclass Test Series

Exam Paper Generator

Online Exam Module