Light is incident on a metallic plate having work function \( 110\times10^{-20} \) J. If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is __________ rad/s. (\( h=6.63\times10^{-34} \) J.s)

A stationary particle breaks into two parts of masses \(m_A\) and \(m_B\) which move with velocities \(v_A\) and \(V_B\) respectively. The ratio of their kinetic energies \(\left(\mathrm{K}_B: \mathrm{K}_{\mathrm{A}}\right)\) is _______.

If three moles of monoatomic gas \(\left(\gamma=\frac{5}{3}\right)\) is mixed with two moles of a diatomic gas \(\left(\gamma=\frac{7}{5}\right)\), the value of adiabatic exponent \(\gamma\) for the mixture is _______.

For a given gas at \(1\,atm\) pressure, \(rms\) speed of the molecules is \(200\,m/s\) at \(127\,^oC.\) At \(2\,atm\) pressure and at \(227\,^oC,\) the \(rms\) speed of the molecules will be

The electric current through a wire varies with time as \(I=I_0+\beta t\). where \(I_0=20 \mathrm{~A}\) and \(\beta=3 \mathrm{~A} / \mathrm{s}\). The amount of electric charge crossed through a section of the wire in \(20 \mathrm{~s}\) is :

Two planets \(A\) and \(B\) of equal mass are having their period of revolutions \(T_{A}\) and \(T_{B}\) such that \(T_{A}=2 T_{B}\). These planets are revolving in the circular orbits of radii \(I_{A}\) and \(I_{B}\) respectively. Which out of the following would be the correct relationship of their orbits?

A particle executes simple harmonic motion. Its amplitude is \(8 \,cm\) and time period is \(6 \,s\). The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ............. \(s\)

\(M\) grams of steam at \(100^{\circ} \mathrm{C}\) is mixed with \(200\; \mathrm{g}\) of ice at its melting point in a thermally insulated container. If it produces liquid water at \(40^{\circ} \mathrm{C}\) [heat of vaporization of water is \(540 \;cal/\mathrm{g}\) and heat of fusion of ice is \(80 \;\text { cal/g }]\) the value of \(\mathrm{M}\) is

A convex lens of refractive index 1.5 and focal length \(f=18 cm\) is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is \(\alpha \times f\). The value of \(\alpha\) is ___________.
(refractive index of water \(=4 / 3\) )

A ball of mass \(160\, g\) is thrown up at an angle of \(60^o\) to the horizontal at a speed of \(10\, m\,s^{-1}\) . The angular momentum of the ball at the highest point of the trajectcry with respect to the point from which the ball is thrown is nearly ........ \(kg\, m^2/s\)  \((g\, = 10\, m\,s^{-2})\)

The diameter of a spherical bob is measured using a vernier callipers. \(9\) divisions of the main scale, in the vernier callipers, are equal to \(10\) divisions of vernier scale. One main scale division is \(1\, {mm}\). The main scale reading is \(10\, {mm}\) and \(8^{\text {th }}\) division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of \(0.04\, {cm}\), then the radius of the bob is \(...... \,\times 10^{-2} \,{cm}\)

A point dipole \(\vec p =  - {p_0}\hat x\) is kept at the origin. The potential and electric field due to this dipole on the \(y-\) axis at a distance \(d\) are, respectively : (Take \(V = 0\) at infinity)