1
JEE Main 2024 (Online) 27th January Morning Shift
Numerical
+4
-1

Four particles each of mass $$1 \mathrm{~kg}$$ are placed at four corners of a square of side $$2 \mathrm{~m}$$. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is _____ $$\mathrm{kgm}^2$$.

2
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively $\left(k_{\text {sph }}: k_{\text {cyl }}\right)$ is $2: \sqrt{x}$. The value of $x$ is ____________ .
3
JEE Main 2023 (Online) 13th April Evening Shift
Numerical
+4
-1

A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be _________ rad s$$^{-2}$$.

4
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $$\pi: 22$$ then, the value of its angular speed will be ____________ $$\mathrm{rad} / \mathrm{s}$$.

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