Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is \(x: y .\) The value of \(x\) is ...... .

A lift of mass \(1600\) kg is supported by thick iron wire. If the maximum stress which the wire can withstand is \(4 \times 10^8\) N/m\(^2\) and its radius is \(4\) mm, then maximum acceleration the lift can take is _______ m/s\(^2\). (take \(g = 10\) m/s\(^2\) and \(\pi = 3.14\))

A fluid is flowing through a horizontal pipe of varying cross-section, with speed \(v\;ms^{-1}\) at a point where the pressure is \(P\) Pascal. At another point where pressure is \(\frac{ P }{2}\) Pascal its speed is \(V\;ms^{-1}\). If the density of the fluid is \(\rho\, kg\, m ^{-3}\) and the flow is streamline, then \(V\) is equal to

The angular frequency of the damped oscillator is given by, \(\omega  = \sqrt {\left( {\frac{k}{m} - \frac{{{r^2}}}{{4{m^2}}}} \right)} \) where \(k\) is the spring constant, \(m\) is the mass of the oscillator and \(r\) is the damping constant. If the ratio \(\frac{{{r^2}}}{{mk}}\) is \(8\%\), the change in time period compared to the undamped oscillator is approximately as follows

Consider two containers \(A\) and \(B\) containing monoatomic gases at the same Pressure \((P)\), Volume \((V)\) and Temperature \((T)\). The gas in \(A\) is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas \(B\) is compressed adiabatically to \(\frac{1}{8}\) of its original volume. The ratio of final pressure of gas in \(B\) to that of gas in \(A\) is ...........

Two radioactive materials \(A\) and \(B\) have decay constants \(25 \lambda\) and \(16 \lambda\) respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \(B\) to that of \(A\) will be "\(e\)" after a time \(\frac{1}{a \lambda}\). The value of \(a\) is \(......\)

The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure What is the value of current at \(t = 4\,s\) ? ............... \(\mu  A\)

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

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