1
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1

$$\mathrm{I_{CM}}$$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $$\mathrm{I_{AB}}$$ is it's moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance $$\frac{2}{3}$$R from center. Where R is the radius of the disc. The ratio of $$\mathrm{I_{AB}}$$ and $$\mathrm{I_{CM}}$$ is $$x:9$$. The value of $$x$$ is _____________.

2
JEE Main 2023 (Online) 24th January Evening Shift
Numerical
+4
-1

A uniform solid cylinder with radius R and length L has moment of inertia I$$_1$$, about the axis of the cylinder. A concentric solid cylinder of radius $$R'=\frac{R}{2}$$ and length $$L'=\frac{L}{2}$$ is carved out of the original cylinder. If I$$_2$$ is the moment of inertia of the carved out portion of the cylinder then $$\frac{I_1}{I_2}=$$ __________.

(Both I$$_1$$ and I$$_2$$ are about the axis of the cylinder)

3
JEE Main 2023 (Online) 24th January Morning Shift
Numerical
+4
-1

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be $$\sqrt x$$ cm. The value of $$x$$ is ________.

4
JEE Main 2022 (Online) 28th July Morning Shift
Numerical
+4
-1

Four identical discs each of mass '$$\mathrm{M}$$' and diameter '$$\mathrm{a}$$' are arranged in a small plane as shown in figure. If the moment of inertia of the system about $$\mathrm{OO}^{\prime}$$ is $$\frac{x}{4} \,\mathrm{Ma}^{2}$$. Then, the value of $$x$$ will be ____________.