1
JEE Main 2024 (Online) 1st February Evening Shift
Numerical
+4
-1
A uniform rod $A B$ of mass $2 \mathrm{~kg}$ and length $30 \mathrm{~cm}$ at rest on a smooth horizontal surface. An impulse of force $0.2 \mathrm{~Ns}$ is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{\pi}{x} \mathrm{~s}$, where $x=$ _______ .
2
JEE Main 2024 (Online) 31st January Evening Shift
Numerical
+4
-1

A body of mass '$$m$$' is projected with a speed '$$u$$' making an angle of $$45^{\circ}$$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $$\frac{\sqrt{2} m u^3}{X g}$$. The value of '$$X$$' is _________.

3
JEE Main 2024 (Online) 31st January Evening Shift
Numerical
+4
-1

Two identical spheres each of mass $$2 \mathrm{~kg}$$ and radius $$50 \mathrm{~cm}$$ are fixed at the ends of a light rod so that the separation between the centers is $$150 \mathrm{~cm}$$. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is $$\frac{x}{20} \mathrm{~kg} \mathrm{m^{2 }}$$, where the value of $$x$$ is ___________.

4
JEE Main 2024 (Online) 30th January Evening Shift
Numerical
+4
-1

Two discs of moment of inertia $$I_1=4 \mathrm{~kg} \mathrm{~m}^2$$ and $$I_2=2 \mathrm{~kg} \mathrm{~m}^2$$, about their central axes & normal to their planes, rotating with angular speeds $$10 \mathrm{~rad} / \mathrm{s}$$ & $$4 \mathrm{~rad} / \mathrm{s}$$ respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is _________ J.