A uniform chain of length \(3\, meter\) and mass \(3\, {kg}\) overhangs a smooth table with \(2\, meter\) laying on the table. If \(k\) is the kinetic energy of the chain in joule as it completely slips off the table, then the value of \({k}\) is (Take \(\left.g=10\, {m} / {s}^{2}\right)\)

A thin smooth rod of length \(L\) and mass \(M\) is rotating freely with angular speed \({\omega _0}\) about an axis perpendicular to the rod and passing through its centre. Two beads of mass \(m\) and negligible size are at the centre of the rod initially. The beads are free to slide along the rod. The angular speed of the system, when the beads reach the opposite ends of the rod will be

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains:

A parallel plate capacitor of capacitance \(2\; F\) is charged to a potential \(V\). The energy stored in the capacitor is \(E_1\). The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is \(E _2\). The ratio \(E _2 / E _1\) is

Determine the charge on the capacitor in the following circuit ................ \(\mu  C\)

Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ .

Identify the correct truth table of the given logical circuit.

Match List-\(I\) with List-\(II\) :-

List - \(I\) (EM-Wave)	List - \(II\) (Wavelength) (Range)
\((A)\) infra-red	\((i)\) \(<10^{-3} \mathrm{~nm}\)
\((B)\) Ultraviolet	\((ii)\) \(400 \mathrm{~nm}\) to \(1 \mathrm{~nm}\)
\((C)\) X-rays	\((iii)\) \(1 \mathrm{~mm}\) to \(700 \mathrm{~nm}\)
\((D)\) Gamma rays	\((iv)\) \(1 \mathrm{~nm}\) to \(10^{-3} \mathrm{~nm}\)

Choose the correct answer from the options given below:

Intensity of sunlight is observed as \(0.092\, {Wm}^{-2}\) at a point in free space. What will be the peak value of magnetic field at that point? \(\left(\sigma_{0}=8.85 \times 10^{-12}\, {C}^{2} \,{N}^{-1} \,{m}^{-2}\right.\) )

A stone is dropped from the top of a building. When it crosses a point \(5\, m\) below the top, another stone starts to fall from a point \(25\, m\) below the top. Both stones reach the bottom of building simultaneously. The height of the building is ..... \(m\).