Two sources of sound \(S_1\) and \(S_2\) produce sound waves of same frequency \(660\, Hz\). A listener is moving from source \(S_1\) towards \(S_2\) with a constant speed \(u\, m/s\) and he hears \(10\, beats/s\). The velocity of sound is \(330\, m/s\). Then, \(u\) equals ... \(m/s\)

In the given figure, an inductor and a resistor are connected in series with a battery of emf \(E\) volt. \(\frac{E^a}{2 b }\,J / s\) represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of \(\frac{ b }{ a }\) will be ............

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws \(25 \%\) more charge from the battery. The dielectric constant of mica is ___________ .

A uniformly charged solid sphere of radius \(R\) has potential \(V_0\) (measured with respect to \(\infty\)) on its surface. For this sphere the equipotential surfaces with potentials \(\frac{{3{V_0}}}{2},\;\frac{{5{V_0}}}{4},\;\frac{{3{V_0}}}{4}\) and \(\frac{{{V_0}}}{4}\) have rasius \(R_1,R_2,R_3\) and \(R_4\) respectively. Then

Two concentric circular coils with radii \(1\,cm\) and \(1000\,cm\), and number of turns \(10\) and \(200\) respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be \(.........\times 10^{-8}\,H\)(Take, \(\pi^2=10\))

A thin prism \(\mathrm{P}_1\) with angle \(4^{\circ}\) made of glass having refractive index 1.54 , is combined with another thin prism \(\mathrm{P}_2\) made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism \(P_2\) in degrees is _______.

A sinusoidal voltage of peak value \(283\, V\) and angular frequency \(320/s\) is applied to a series \(LCR\) circuit. Given that \(R\, = 5\,\Omega \) , \(L\,= 25\, mH\) and \(C\, = 1000\, \mu F\). The total impedance, and phase difference between the voltage across the source and the current will respectively be

Which of the following statements is false?

A poly-atomic molecule ( \(C_V=3 R, C_P=4 R\), where \(R\) is gas constant) goes from phase space point \(\mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right.\) \(\left.\mathrm{Pa}, \mathrm{V}_{\mathrm{C}}=8 \times 10^{-6} \mathrm{~m}^3\right)\). A to B is an adiabatic path and \(B\) to \(C\) is an isothermal path. The net heat absorbed per unit mole by the system is :

A particle is moving along a circular path with a constant speed of \(10\,ms^{-1}.\) What is the magnitude of the change in velocity of the particle, when it moves through an angle of \(60^{o}\) around the centre of the circle .......... \(m/s\)

The volume of an ideal gas increases 8 times and temperature becomes (1/4) of initial temperature during a reversible change. If there is no exchange of heat in this process (\( \Delta Q=0 \)) then identify the gas from the following options: