A metallic conductor of length \(1\; m\) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \(5 \;rad / s\). If the horizontal component of earth's magnetic field is \(0.2 \times 10^{-4} \;T\), then emf induced between the two ends of the conductor is .............

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:

The region between two concentric spheres ofradii '\(a\)' and '\(b\)', respectively (see figure), have volume charge density \(\rho = \frac{A}{r}\) where \(A\) is a constant and \(r\) is the distance from the centre. At the centre of the spheres is a point charge \(Q\). The value of \(A\) such that the electric field in the region between the spheres will be constant, is :

An iron rod of volume \(10^{-3}\, m ^{3}\) and relative permeability \(1000\) is placed as core in a solenoid with \(10\) \(turns/cm.\) If a current of \(0.5\, A\) is passed through the solenoid, then the magnetic moment of the rod will be\(...........Am^2\)

A block of mass \(m\) slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given \({m}=8 \,{kg}, {M}=16\, {kg}\) Assume all the surfaces shown in the figure to be frictionless.

There are \(100\) divisions on the circular scale of a screw gauge of pitch \(1 \mathrm{~mm}\). With no measuring quantity in between the jaws, the zero of the circular scale lies \(5\) divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found the \(4\) linear scale divisions are clearly visible while \(60\) divisions on circular scale coincide with the reference line. The diameter of the wire is _______.

Two bodies of masses \(1\, kg\) and \(4\, kg\) are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency \(25\, rad/s\), and amplitude \(1.6\, cm\) while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is ..... \(N\) ( take \(g = 10\, ms^{-2}\))

A massless square loop, of wire of resistance \(10\,\Omega\). supporting a mass of \(1\,g\). hangs vertically with one of its sides in a uniform magnetic field of \(10^3\, G\), directed outwards in the shaded region. A dc voltage \(V\) is applied to the loop. For what value of V. the magnetic force will exactly balance the weight of the supporting mass of \(1\,g\) ? (If sides of the loop \(=10\,cm , g =10\,ms ^{-2}\) )

Given below are two statements: Statement \(I\): An \(AC\) circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement \(II\): An \(AC\) circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer from the options given below

A diatomic gas \((\gamma=1.4)\) does 100 J of work when it is expanded isobarically. Then the heat given to the gas _________ J.

Figure shows charge \((q)\) versus voltage \((V)\) graph for series and parallel combination of to given capacitors. The capacitances are

By what percentage will the illumination of the lamp decrease if the current drops by \(20 \%\) ?

An air bubble of diameter \(6\,mm\) rises steadily through a solution of density \(1750\,kg / m ^3\) at the rate of \(0.35\,cm / s\). The co-efficient of viscosity of the solution (neglect density of air) is \(..........\,Pas\) (given, \(g =10\,ms ^{-2}\))