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 _______.

A rod with circular cross-section area \(2\,cm ^2\) and length \(40\,cm\) is wound uniformly with \(400\) turns of an insulated wire. If a current of \(0.4\,A\) flows in the wire windings, the total magnetic flux produced inside windings is \(4\,\pi \times 10^{-6}\,Wb\). The relative permeability of the rod is (Given : Permeability of  vacuum \(\left.\mu_0=4 \pi \times 10^{-7} \;NA ^{-2}\right)\)

A galvanometer having coil resistance \(10 \ \Omega\) shows a full scale deflection for a current of \(3 \mathrm{~mA}\). For it to measure a current of \(8 \mathrm{~A}\), the value of the shunt should be:

Given below are two statements: Statement \(I:\) Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement \(II:\) Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light. In the light of above statements, choose the correct answer from the options given below:

A single turn current loop in the shape of a right angle triangle with sides \(5\,cm , 12\,cm , 13\,cm\) is carrying a current of \(2\,A\). The loop is in a uniform magnetic field of magnitude \(0.75\,T\) whose direction is parallel to the current in the \(13\,cm\) side of the loop. The magnitude of the magnetic force on the \(5\,cm\) side will be \(\frac{ x }{130}\,N\). The value of \(x\) is \(..........\)

A cylindrical rod of length 1 m and radius 4 cm is mounted vertically. It is subjected to a shear force of \(10^5 \mathrm{~N}\) at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement \(\theta\) of the rod axis from its original position would be : (shear moduli, \(\left.\mathrm{G}=10^{10} \mathrm{~N} / \mathrm{m}^2\right)\)

A potentiometer wire of length \(10 \,m\) and resistance\(20 \,\Omega\) is connected in series with a \(25 \,V\) battery and an external resistance \(30\, \Omega\). A cell of emf \(E\) in secondary circuit is balanced by \(250\, cm\) long potentiometer wire. The value of \(E\) (in volt) is \(\frac{x}{10}\). The value of \(x\) is.......

From the top of a tower, a ball is thrown vertically upward which reaches the ground in \(6 \,s\). A second ball thrown vertically downward from the same position with the same speed reaches the ground in \(1.5\, s\). A third ball released, from the rest from the same location, will reach the ground in........ \(s\).

The frequency of oscillation of a mass \(m\) suspended by a spring is \(v_1\). If the length of the spring is cut to half, the same mass oscillates with frequency \(v_2\). The value of \(v_2/v_1\) is ________.

A small square loop of side \('a'\) and one turn is placed inside a larger square loop of side \({b}\) and one turn \((b \gg a)\). The two loops are coplanar with thei centres coinciding. If a current \(I\) is passed in the square loop of side \('b',\) then the coefficient of mutual inductance between the two loops is

The speed of light in media \('A'\) and \('B'\) are \(2.0 \times\) \(10^{10} \,cm / s\) and \(1.5 \times 10^{10} \,cm / s\) respectively. A ray of light enters from the medium \(B\) to \(A\) at an incident angle ' \(\theta\) '. If the ray suffers total internal reflection, then

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is \(2.4\) \(\mu\)m. If the experiment is carried out in another medium having refractive index \(1.2\), the fringe width will be _____ \(\mu\)m.

Four \(NOR\) gates are connected as shown in figure. The truth table for the given figure is :