The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the \(5^{\text {th }}\) excited state of a hydrogen atom is _______.

In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are \(50\) divisions on the circular scale, and the main scale moves by \(0.5 \,{mm}\) on a complete rotation. For a particular observation the reading on the main scale is \(5\, {mm}\) and the \(20^{\text {th }}\) division of the circular scale coincides with reference line. Calculate the true reading. (in \({mm}\))

A square loop of side \(2\, a ,\) and carrying current I, is kept in \(XZ\) plane with its centre at origin. A long wire carrying the same current \(I\) is placed parallel to the \(z-\)axis and passing through the point \((0, b, 0),(b>>a)\). The magnitude of the torque on the loop about \(z-\)axis is given by:

A smooth wire of length \(2\pi r\) is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed \(\omega\) about the vertical diameter \(AB\), as shown in figure, the bead is at rest with respect to the circular ring at position \(P\) as shown. Then the value of \(\omega^2\) is equal to

The equation of stationary wave is \(\mathrm{y}=2 \mathrm{a} \sin \left(\frac{2 \pi \mathrm{nt}}{\lambda}\right) \cos \left(\frac{2 \pi \mathrm{x}}{\lambda}\right)\) Which of the following is NOT correct?

A tuning fork \(A\) of unknown frequency produces \(5\, beats/s\) with a fork of known frequency \(340\, Hz\). When fork \(A\) is filed, the beat frequency decreases to \(2\, beats/s.\) What is the frequency of fork \(A\) ? (in \(Hz\))

The value closest to the thermal velocity of a Helium atom at room temperature \((300\,K)\)in \(ms^{-1}\) is \([k_B\, = 1 .4\times10^{-23}\,J/K;\, m_{He}\, = 7\times10^{-27}\,kg]\)

An element \(\Delta l=\Delta \mathrm{xi}\) is placed at the origin and carries a large current \(\mathrm{I}=10 \mathrm{~A}\). The magnetic field on the \(y\)-axis at a distance of \(0.5 \mathrm{~m}\) from the elements \(\Delta \mathrm{x}\) of \(1 \mathrm{~cm}\) length is _______.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \(\left(R / \sqrt{R^2+\omega^2 L^2}\right)\), where \(\omega\) is frequency of the supply across resistor \(R\) and inductor L . If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In the light of the above statements, choose the most appropriate answer from the options given below :

Water droplets are coming from an open tap at particular rate. The spacing between a droplet observed at \(4^{{th}}\;second\) after its fall to the next droplet is \(34.3 \,{m}\). At what rate the droplets are coming from the tap ? (Take \(g=9.8\, {m} / {s}^{2}\))

Two parallel, long wires are kept \(0.20\,m\) apart in vacuum, each carrying current of \(x\) in the same direction. If the force of attraction per meter of each wire is \(2 \times 10^{-6}\,N\), then the value of \(x\) is approximately

The potential energy of a particle changes with distance \(x\) from a fixed origin as \(V = \dfrac{A\sqrt{x}}{x + B}\), where \(A\) and \(B\) are constant with appropriate dimensions. The dimensions of \(AB\) are _______.

Figure shows a part of an electric circuit. The potentials at points \(a , b\) and \(c\) are \(30\,V , 12\,V\) and \(2\,V\) respectively. The current through the \(20 \Omega\) resistor will be \(........\,A\)