The end correction of a resonance column is \(1\,cm.\)  If the shortest length resonating with the tuning fork is \(10\,cm,\)  the next resonating length should be ..... \(cm\)

The difference between threshold wavelengths for two metal surfaces \(A\) and \(B\) having work function \(\phi_A=9\,eV\) and \(\phi_{ B }=4.5\,eV\) in \(nm\) is:(Given, \(hc =1242\,eV\,nm\))

A Carnot freezer takes heat from water at \(0\,^oC\) inside it and rejects it to the room at a temperature of \(27\,^oC\). The latent heat of ice is \(336 \times 10^3\, J\,kg^{-1}\).  lf \(5\, kg\) of water at \(0\,^oC\) is converted into ice at  \(0\,^oC\) by the freezer, then the energy consumed by the freezer is close to

A Copper \((Cu)\) rod of length \(25\, {cm}\) and cross- sectional area \(3\, {mm}^{2}\) is joined with a similar Aluminium \((Al)\) rod as shown in figure. Find the resistance of the combination between the ends \(A\) and \(B\) (in \({m} \Omega\)) (Take Resistivity of Copper \(=1.7 \times 10^{-8}\, \Omega \,{m}\), Resistivity of Aluminium \(=2.6 \times 10^{-8}\, \Omega \,{m}\) )

A \(2\,meter\) long scale with least count of \(0.2\,cm\) is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at \(80\,cm\) mark and \(1\,m\) mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at \(180\,cm\) mark. The \(\%\) error in the estimation of focal length is

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is \(1\,kg\), the angular frequency is \(\omega_1\). When the mass block is \(2\,kg\) the angular frequency is \(\omega_2\). The ratio \(\omega_2 / \omega_1\) is

A flask contains Hydrogen and Argon in the ratio \(2: 1\) by mass. The temperature of the mixture is \(30^{\circ} C\). The ratio of average kinetic energy per molecule of the two gases ( \(K\) argon/ \(K\) hydrogen) is: (Given: Atomic Weight of \(Ar = 39.9\))

An \(\alpha\)-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength: