A wire of mass M is bent into a circular shap | vedclass

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

Question

(A) wire bent into a circular shape acts as a thin ring of mass $M$ and radius $R$.For a ring,the moment of inertia about an axis passing through its

Vedclass · Accepted Answer

$\frac{MR^2}{2}$

Vedclass · Answer

(A) wire bent into a circular shape acts as a thin ring of mass $M$ and radius $R$.For a ring,the moment of inertia about an axis passing through its center and perpendicular to its plane is $I_{cm} = MR^2$.According to the perpendicular axis theorem,$I_z = I_x + I_y$.Since the ring is symmetric,the moment of inertia about any diameter is the same,so $I_x = I_y = I_d$.Therefore,$MR^2 = I_d + I_d = 2I_d$.Solving for $I_d$,we get $I_d = \frac{MR^2}{2}$.

$A$ wire of mass $M$ is bent into a circular shape of radius $R$. What is the moment of inertia about its diameter?

Similar Questions

Calculate the moment of inertia of the system shown in the figure about the axis of rotation $XX'$.

If a wheel rotating with a constant angular speed experiences a break during its motion,what happens to its radius of gyration?

Weights of $1 \ kg$ and $4 \ kg$ are placed at the $20 \ cm$ and $70 \ cm$ marks of a light meter scale,respectively. What is the moment of inertia in $kg \ m^2$ about an axis perpendicular to the scale and passing through the $100 \ cm$ mark?

On which of the following does the moment of inertia of an object $NOT$ depend?

The ratio of the radii of two solid spheres of same mass is $2:3$. The ratio of the moments of inertia of the spheres about their diameters is

Vedclass Test Series

Exam Paper Generator

Online Exam Module