If the radius of gyration of a thin circular | vedclass

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

Question

(A) The moment of inertia of a thin circular ring of mass $M$ and radius $R$ about an axis passing through its centre and perpendicular to its plane i

Vedclass · Accepted Answer

$10 \,cm$

Vedclass · Answer

(A) The moment of inertia of a thin circular ring of mass $M$ and radius $R$ about an axis passing through its centre and perpendicular to its plane is $I_z = MR^2$. The radius of gyration $k_z$ is given by $I_z = Mk_z^2$, so $k_z = R = 10 \sqrt{2} \,cm$.The moment of inertia of the ring about its diameter is $I_d = \frac{1}{2} MR^2$. The radius of gyration $k_d$ about the diameter is given by $I_d = Mk_d^2$.Thus, $Mk_d^2 = \frac{1}{2} MR^2$, which implies $k_d = \frac{R}{\sqrt{2}}$.Substituting the value of $R = 10 \sqrt{2} \,cm$, we get $k_d = \frac{10 \sqrt{2}}{\sqrt{2}} = 10 \,cm$.

If the radius of gyration of a thin circular ring about an axis passing through its centre and perpendicular to its plane is $10 \sqrt{2} \,cm$, then its radius of gyration about its diameter is

Similar Questions

For the adjoining diagram,the incorrect relation between $I_{1}, I_{2}$ and $I_{3}$ is ($I$ = moment of inertia).

Two circular loops $P$ and $Q$ of radii $r$ and $nr$ are made respectively from a uniform wire. The moment of inertia of loop $Q$ about its axis is four times that of loop $P$ about its axis. The value of $n$ is

The radius of gyration of a body depends upon:

Four point masses each of mass $m$ are placed at the corners of a square $ABCD$ of side length $\ell$. What is the moment of inertia about an axis passing through $A$ and parallel to $BD$?

Four masses are fixed on a massless rod as shown in the figure. The moment of inertia about the axis $P$ is about ....... $kg \cdot m^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module