Water flows into a large tank with flat bottom at the rate of \({10^{ - 4}}\,{m^3}{s^{ - 1}}\). Water is also leaking out of a hole of area \(1\, cm^2\) at its bottom. If the height of the water in the tank remains steady, then this height is........ \(cm\)

A \(750\, Hz,\) \(20\) \(V\) (rms ) source is connected to a resistance of \(100\, \Omega\) an inductance of \(0.1803\, H\) and a capacitance of \(10\mu ,\) \(F\) all in series. The time in which the resistance (heat capacity \(2 J /{ }^{\circ} C\) ) will get heated by \(10^{\circ} C\). (assume no \(105 s\) of heat to the surroundings) is close to\(.....s\)

A body of mass \(10\,kg\) is moving with an initial speed of \(20\,m / s\). The body stops after \(5\,s\) due to friction between body and the floor. The value of the coefficient of friction is (Take acceleration due to gravity \(g =10\; ms ^{-2}\))

A parallel plate capacitor is formed by two plates each of area \(30 \pi\, cm ^{2}\) separated by \(1\, mm\). A material of dielectric strength \(3.6 \times 10^{7} \,Vm ^{-1}\) is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is \(7 \times 10^{-6}\, C\), the value of dielectric constant of the material is \(\left\{ Use : \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right\}\)

A particle having charge \(10^{-9}\) C moving in \(x\)-\(y\) plane in fields of \(0.4\hat{j}\) N/C and \(4 \times 10^{-3} \hat{k}\) T experiences a force of \((4\hat{i} + 2\hat{j}) \times 10^{-10}\) N. The velocity of the particle at that instant is _______ m/s.

If the magnetic field in a plane electromagnetic wave is given by \(\overrightarrow{\mathrm{B}}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{j}}\; \mathrm{T}\) then what will be expression for electric field?

The energy of a system is given as \(\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}\), where t is the time and \(\beta=0.3 \mathrm{~s}^{-1}\). The errors in the measurement of \(\alpha\) and \(t\) are \(1.2 \%\) and \(1.6 \%\), respectively. At \(t=5 \mathrm{~s}\), maximum percentage error in the energy is :

The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of \(176 rad / s\). The frequency of this simple harmonic oscillator is _________ Hz. \(\left[\right.\) take \(\left.\pi=\frac{22}{7}\right]\)

A tuning fork of frequency \(340\,Hz\) resonates in the fundamental mode with an air column of length \(125\,cm\) in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is________ \(cm\) (Velocity of sound in air is \(340\,ms ^{-1}\) )

Two separate wires \(A\) and \(B\) are stretched by \(2 \,mm\) and \(4\, mm\) respectively, when they are subjected to a force of \(2\, N\). Assume that both the wires are made up of same material and the radius of wire \(B\) is 4 times that of the radius of wire \(A\). The length of the wires \(A\) and \(B\) are in the ratio of \(a : b\). Then \(a / b\) can be expressed as \(1 / x\) where \(x\) is

Consider an electrical circuit containing a two way switch \(^{\prime}{S}^{\prime}\). Initially \({S}\) is open and then \({T}_{1}\) is connected to \({T}_{2} .\) As the current in \({R}=6 \,\Omega\) attains a maximum value of steady state level, \({T}_{1}\) is disconnected from \({T}_{2}\) and immediately connected to \({T}_{3} .\) Potential drop across \({r}=3\, \Omega\) resistor immediately after \(T_{1}\) is connected to \(T_{3}\) is \(....\,V.\) (Round off to the Nearest Integer)

The resistance of the meter bridge \(AB\) in given figure is \(4\,\Omega \). With a cell of emf  \(\varepsilon \, = 0.5\,\,V\) and rheostat resistance \(R_h = 2\,\Omega \) the null point is obtained at some point \(J.\) When the cell is replaced by another one of emf \(\varepsilon \, = {\varepsilon _2}\) the same null point \(J\) is found for \(R_h = 6\,\Omega .\) The \(emf\)  \({\varepsilon _2}\) is ................. \(V\)