When a certain photosensitive surface is illuminated with monochromatic light of frequency \(v\) , the stopping potential for the photo current is \(-V_0/2.\) When the surface is illuminated by monochromatic light of frequency \(v/2,\) the stopping potential is \(-V_0.\) The threshold frequency for photoelectric emission is

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed \(v\). If \(x\) is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to \(x^\alpha\), where \(\alpha\) is _____.

Assume there are two identical simple pendulum Clocks\(-1\) is placed on the earth and Clock\(-2\) is placed on a space station located at a height \(h\) above the earth surface. Clock\(-1\) and Clock\(-2\) operate at time periods \(4\,s\) and \(6\,s\) respectively. Then the value of \(h\) is \(....km\) (consider radius of earth \(R _{ E }=6400\,km\) and \(g\) on earth \(10\,m / s ^{2}\) )

A heat source at \(T = 10^3\, K\) is connected to another heat reservoir at \(T = 10^2\, K\) by a copper slab which is \(1\, m\) thick. Given that the thermal conductivity of copper is \(0.1\, WK^{-1}\, m^{-1}\), the energy flux through it in the steady state is ........... \(Wm^{-2}\)

A bullet is fired into a fixed target looses one third of its velocity after travelling \(4 \mathrm{~cm}\). It penetrates further \(\mathrm{D} \times 10^{-3} \mathrm{~m}\) before coming to rest. The value of \(D\) is:

A parallel plate capacitor of capacitance \(90\ pF\) is connected to a battery of \(emf\) \(20\ V\). If a dielectric material of dielectric constant \(K = \frac{5}{3}\) is inserted between the plates, the magnitude of the induced charge will be.......\(n \) \(C\)

Two blocks (\(P\) and \(Q\)) with respectively masses \(2\) kg and \(1.5\) kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (\(S\)), as shown in the figure below. Block \(P\) is positioned on the top surface which has no friction and block \(Q\) is in contact with side-surface, having coefficient friction \(\mu\). The cube (\(S\)) moves towards the right with acceleration of \(\dfrac{g}{2}\), where \(g\) is gravitational acceleration. During this movement the block \(P\) and \(Q\) remain stationary. The value of \(\mu\) is _______. (take \(g = 10\) m/s\(^2\))

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion:

What is the dimensional formula of \(a b^{-1}\) in the equation? \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where letters have their usual meaning.

A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same \(P, V, T\). Heating is started from left side until pressure changes to \(\dfrac{27P}{8}\). If initial volume of each compartment was \(9\) litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas \(C_P/C_V = 1.5\))

The temperature of equal masses of three different liquids \({x}, {y}\) and \({z}\) are \(10^{\circ} {C}, 20^{\circ} {C}\) and \(30^{\circ} {C}\) respectively. The temperature of mixture when \({x}\) is mixed with \({y}\) is \(16^{\circ} {C}\) and that when \({y}\) is mixed with \(z\) is \(26^{\circ} {C}\). The temperature of mixture when \(x\) and \(z\) are mixed will be ...... \(^{\circ} {C}\)

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant \(K\) is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is \(\frac{3}{4} d\), where \('d'\) is the separation between the plates of parallel plate capacitor. The new capacitance \((C')\) in terms of original capacitance \(\left( C _{0}\right)\) is given by the following relation

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed \(v,\) he sees that rain drops are coming at an angle \(60^{\circ}\) from the horizontal. On further increasing the speed of the car to \((1+\beta) v ,\) this angle changes to \(45^{\circ} .\) The value of \(\beta\) is close to\(......\)