1
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 ___________.

2
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.

3
JEE Main 2024 (Online) 30th January Morning Shift
Numerical
+4
-1

Consider a Disc of mass $$5 \mathrm{~kg}$$, radius $$2 \mathrm{~m}$$, rotating with angular velocity of $$10 \mathrm{~rad} / \mathrm{s}$$ about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is ________ J.

4
JEE Main 2024 (Online) 29th January Evening Shift
Numerical
+4
-1

A body of mass $$5 \mathrm{~kg}$$ moving with a uniform speed $$3 \sqrt{2} \mathrm{~ms}^{-1}$$ in $$X-Y$$ plane along the line $$y=x+4$$. The angular momentum of the particle about the origin will be _________ $$\mathrm{kg} \mathrm{~m}^2 \mathrm{~s}^{-1}$$.