1
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 ____________.

2
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)

3
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 ___________.

4
JEE Main 2022 (Online) 27th June Evening Shift
Numerical
+4
-1

A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be $${1 \over 2}\sqrt {xgh}$$ m/s. The value of x is ___________.