A string of length \(1\, m\) and mass \(5\, g\) is fixed at both ends. The tension in the string is \(8.0\, N\). The string is set into vibration using an external vibrator of frequency \(100\, Hz\). The separation between successive nodes on the string is close to .... \(cm\)

A capacitor has air as dielectric medium and two conducting plates of area \(12 \mathrm{~cm}^2\) and they are \(0.6 \mathrm{~cm}\) apart. When a slab of dielectric having area \(12 \mathrm{~cm}^2\) and \(0.6 \mathrm{~cm}\) thickness is inserted between the plates, one of the conducting plates has to be moved by \(0.2 \mathrm{~cm}\) to keep the capacitance same as in previous case. The dielectric constant of the slab is _______. (Given \(\left.\epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\)

The time period of a satellite revolving around earth in a given orbit is \(7 \,hours\). If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be ...... \(hours\)

If the collision frequency of hydrogen molecules in a closed chamber at \(27^{\circ} \mathrm{C}\) is \(\mathrm{Z}\), then the collision frequency of the same system at \(127^{\circ} \mathrm{C}\) is _______.

A bat moving at \(10\,ms^{-1}\) towards a wall sends a sound signal of \(8000\,Hz\) towards it. On reflection it hears a sound of frequency \(f\). The value of \(f\) in \(Hz\) is close to (speed of sound \(= 320\,ms^{-1}\) )

Time taken by light to travel in two different materials \(A\) and \(B\) of refractive indices \(\mu_{A}\) and \(\mu_{B}\) of same thickness is \(t_{1}\) and \(t_{2}\) respectively. If \(t_{2}-t_{1}=5 \times 10^{-10}\) s and the ratio of \(\mu_{A}\) to \(\mu_{B}\) is \(1: 2\). Then the thickness of material, in meter is: (Given \(v_{A}\) and \(v_{B}\) are velocities of light in \(A\) and \(B\) materials respectively).

If one mole of an ideal gas at \(\left( P _{1}, V _{1}\right)\) is allowed to expand reversibly and isothermally (\(A\) to \(B\) ) its pressure is reduced to one-half of the original pressure (see \(figure\)). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value \(( B \rightarrow C ) .\) Then it is restored to its initial state by a reversible adiabatic compression (\(C\) to \(A\)). The net workdone by the gas is equal to  ...... .

What will be the magnitude of electric field at point \(O\) as shown in figure ? Each side of the figure is \(I\) and perpendicular to each other.

Match List-\(I\) with List-\(II\) Choose the correct answer from the options given below :

As per the given figure, two blocks each of mass \(250\,g\) are connected to a spring of spring constant \(2\,Nm ^{-1}\). If both are given velocity \(V\) in opposite directions, then maximum elongation of the spring is:

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of \(x\) is ______.

A potentiometer wire \(AB\) having length \(L\) and resistance \(12\, r\) is joined to a cell \(D\) of \(emf\) \(\varepsilon \) and internal resistance \(r\). A cell \(C\) having \(emf\) \(\varepsilon /2\) and internal resistance \(3r\) is connected. The length \(AJ\) at which the galvanometer as shown in figure shows no deflection is

In an experiment on photoelectric effect, a student plots stopping potential \(V_0\) against reciprocal of the wavelength \(\lambda \) of the incident light for two different metals \(A\) and \(B\). These are shown in the figure Looking at the graphs, you can most appropriately say that