1
JEE Main 2022 (Online) 27th July Morning Shift
Numerical
+4
-1

A pulley of radius $$1.5 \mathrm{~m}$$ is rotated about its axis by a force $$F=\left(12 \mathrm{t}-3 \mathrm{t}^{2}\right) N$$ applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is $$4.5 \mathrm{~kg} \mathrm{~m}^{2}$$, the number of rotations made by the pulley before its direction of motion is reversed, will be $$\frac{K}{\pi}$$. The value of K is ___________.

2
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ___________ $$\mathrm{m}$$.

Given, the length of the rod is $$10 \sqrt{3} \mathrm{~m}$$.

3
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1

A disc of mass $$1 \mathrm{~kg}$$ and radius $$\mathrm{R}$$ is free to rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be $$4 \sqrt{\frac{x}{3 R}} \,\operatorname{rad}{s}^{-1}$$ where $$x=$$ ____________. $$\left(g=10 \mathrm{~ms}^{-2}\right)$$

4
JEE Main 2022 (Online) 25th July Evening Shift
Numerical
+4
-1

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $$\sqrt x$$ m. The value of x is ____________.

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