A thin wire of length l and mass M is bent in | vedclass

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

Question

(D) The length of the wire is $l$,so the radius $R$ of the semicircle is given by $\pi R = l$,which implies $R = \frac{l}{\pi}$.The moment of inertia

Vedclass · Accepted Answer

$\frac{M l^2}{2 \pi^2}$

Vedclass · Answer

(D) The length of the wire is $l$,so the radius $R$ of the semicircle is given by $\pi R = l$,which implies $R = \frac{l}{\pi}$.The moment of inertia of a thin wire (or ring) of mass $M$ and radius $R$ about an axis passing through its center and perpendicular to its plane is $I = MR^2$.For a semicircle,the moment of inertia about the diameter (the axis passing through the ends) is half of the moment of inertia of the full ring about its center,because the mass is distributed symmetrically.Thus,$I = \frac{1}{2} M R^2$.Substituting $R = \frac{l}{\pi}$ into the equation:$I = \frac{1}{2} M \left(\frac{l}{\pi}\right)^2 = \frac{M l^2}{2 \pi^2}$.

$A$ thin wire of length $l$ and mass $M$ is bent in the form of a semicircle. What is its moment of inertia about an axis passing through the ends of the wire?

Similar Questions

Which branch of science is associated with the development and cultivation of forests?

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 \ s$. In another $10 \ s$,it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals:

The geometry of $ClO_3^-$,according to valence shell electron pair repulsion $(VSEPR)$ theory will be

The equation of the sphere passing through the points $(1,0,0)$,$(0,1,0)$,and $(1,1,1)$ and having the smallest radius is:

Chloroethane reacts with $X$ to form diethyl ether. What is $X$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module