In a photoelectric effect experiment, the graph of stopping potential \(V\) versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased

In the following circuit, the battery has an emf of \(2\mathrm{V}\) and an internal resistance of \(\frac{2}{3}\  \Omega\). The power consumption in the entire circuit is _______ \(W\).

In the given circuit, \(C _1=2\,\mu F , C _2=0.2\,\mu F\), \(C _3=2\,\mu F , C _4=4\,\mu F,\) \(C _5=2\,\mu F , C _6=2\,\mu F\), the charge stored on capacitor \(C _4\) is \(.....\mu C\).

Let \(\sigma\) be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region \(E_{ I }, E_{ II }\) and \(E_{III}\) are

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be \(....m\) Given, the length of the rod is \(10 \sqrt{3} m\).

A ball of mass \(4\, kg\), moving with a velocity of \(10\, ms ^{-1}\), collides with a spring of length \(8\, m\) and force constant \(100\, Nm ^{-1}\). The length of the compressed spring is \(x\, m\). The value of \(x\), to the nearest integer, is ........ .

An object of mass 8 kg is hanging from one end of a uniform rod \(C D\) of mass 2 kg and length 1 m pivoted at its end \(C\) on a vertical wall as shown in figure. It is supported by a cable \(A B\) such that the system is in equilibrium. The tension in the cable is:
(Take \(g=10 m s ^{-2}\) )

A pressure-pump has a horizontal tube of cross-sectional area \(10\,cm ^{2}\) for the outflow of water at a speed of \(20\,m / s\). The force exerted on the vertical wall just in front of the tube which stops water horizontally flowing out of the tube, is \(...N\) [given : density of water \(=1000\,kg / m ^{3}\) ]

A solenoid having area \(A\) and length ' \(l\) ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

A spherical shell of \(1 \,kg\) mass and radius \(R\) is rolling with angular speed \(\omega\) on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the origin \(O\) is \(\frac{a}{3} R^{2} \omega\). The value of a will be ..............

Three equal masses \(m\) are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At \(t=0\), they are given an initial velocity \(\vec{V}_A=V_0 \overrightarrow{A C}, \vec{V}_B=V_0 \overrightarrow{B A}\) and \(\vec{V}_C=V_0 \overrightarrow{C B}\). Here, \(\overrightarrow{A C}, \overrightarrow{C B}\) and \(\overrightarrow{B A}\) are unit vectors along the edges of the triangle. If the three masses interact gravitationally, then the magnitude of the net angular momentum of the system at the point of collision is :

Surface tension of a soap bubble is \(2.0 \times 10^{-2}\; Nm ^{-1}\). Work done to increase the radius of soap bubble from \(3.5\; cm\) to \(7\; cm\) will be \(.........\times 10^{-4}\,J\) [Take \(\pi=\frac{22}{7}\) ]

An electron, a doubly ionized helium ion \(\left( He ^{++}\right)\) and a proton are having the same kinetic energy. The relation between their respective de\(-\)Broglie wavelengths \(\lambda_{ e }, \lambda_{ He ^{++}}\) and \(\lambda_{ P }\) is