1. Tardigrade
  2. Question
  3. Physics
  4. From a circular card board of uniform thickness and mass M, a square disc of maximum possible area is cut. If the moment of inertia of the square with the axis of rotation at the centre and perpendicular to the plane of the disc is (Ma2/6) , the radius of the circular card board is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. From a circular card board of uniform thickness and mass M, a square disc of maximum possible area is cut. If the moment of inertia of the square with the axis of rotation at the centre and perpendicular to the plane of the disc is $\frac{Ma^2}{6}$ , the radius of the circular card board is

KEAMKEAM 2018System of Particles and Rotational Motion

Solution:

According to the question,
image
In the triangular $O A B$,
$(O B)^{2}=(O A)^{2}+(A B)^{2}$
or $r^{2}=\left(\frac{a}{2}\right)^{2}+\left(\frac{a}{2}\right)^{2}$
$r=\sqrt{\frac{2 a^{2}}{4}}=\frac{a}{\sqrt{2}}$