1
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1

Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure). The moment of inertia of the system, about an axis passing through the point O and perpendicular to the plane of the square, is ______________ kg m2.

2
JEE Main 2022 (Online) 29th June Evening Shift
Numerical
+4
-1

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1. The same rod is bent into a ring and its moment of inertia about a diameter is I2. If $${{{I_1}} \over {{I_2}}}$$ is $${{x{\pi ^2}} \over 3}$$, then the value of x will be ____________.

3
JEE Main 2022 (Online) 28th June Evening Shift
Numerical
+4
-1

A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ____________ N.

(Take g = 10 ms$$-$$2)

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

The position vector of 1 kg object is $$\overrightarrow r = \left( {3\widehat i - \widehat j} \right)m$$ and its velocity $$\overrightarrow v = \left( {3\widehat j + \widehat k} \right)m{s^{ - 1}}$$. The magnitude of its angular momentum is $$\sqrt x$$ Nm where x is ___________.