1
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $$\sqrt{\frac{2}{x}}$$. The value of $$x$$ is ___________.

2
JEE Main 2023 (Online) 6th April Morning Shift
Numerical
+4
-1

Two identical solid spheres each of mass $$2 \mathrm{~kg}$$ and radii $$10 \mathrm{~cm}$$ are fixed at the ends of a light rod. The separation between the centres of the spheres is $$40 \mathrm{~cm}$$. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is __________ $$\times 10^{-3} \mathrm{~kg}~\mathrm{m}^{2}$$

3
JEE Main 2023 (Online) 1st February Evening Shift
Numerical
+4
-1

Moment of inertia of a disc of mass '$$M$$' and radius '$$R$$' about any of its diameter is $$\frac{M R^{2}}{4}$$. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, $$\frac{x}{2}$$ MR$$^{2}$$. The value of $$x$$ is ___________.

4
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1

A solid cylinder is released from rest from the top of an inclined plane of inclination $$30^{\circ}$$ and length $$60 \mathrm{~cm}$$. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is __________ $$\mathrm{ms}^{-1}$$. (Given $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$)