The magnetic field associated with a light wave is given, at the origin, by \(B = B_0 [sin\,(3.14 \times 10^7)\,ct\,+\,sin\,(6.28 \times 10^7)\,ct]\) If this light falls on a silver plate having a work function of \(4.7\,eV,\) what will be the maximum kinetic energy of the photo electrons? .............. \(eV\)

The equation of wave is given by \(Y=10^{-2} \sin 2 \pi\left(160 t-0.5 x+\frac{\pi}{4}\right)\) Where \(x\) and \(Y\) are in \(m\) and \(t\) in \(s\). The speed of the wave is \(.....\,km h ^{-1}\)

Light ray incident along a vector \(\vec{AO}\) \((\vec{AO} = 2\hat{i}-3\hat{j})\) emerges out along vector \(\vec{OB}\) \((\vec{OB} = C\hat{i}-4\hat{j})\) as shown in the figure below. The value of \(C\) is ________.

Current passing through a wire as function of time is given as \(\mathrm{I}(\mathrm{t})=0.02 \mathrm{t}+0.01 \mathrm{~A}\). The charge that will flow through the wire from \(t=1 s\) to \(t=2 s\) is :

To get output ‘\(1\)’ at \(R\), for the given logic gate circuit the input values must be

A particle of mass \(20\,g\) is released with an initial velocity \(5\,m/s\) along the curve from the point \(A,\) as shown in the figure. The point \(A\) is at height \(h\) from point \(B.\) The particle slides along the frictionless surface. When the particle reaches point \(B,\) its angular momentum about \(O\) will be ......... \(kg - m^2/s\). [Take \(g = 10\,m/s^2\) ]

A positive point charge is released from rest at a distance \(r_0\) from a positive line charge with uniform density. The speed \((v)\) of the point charge, as a function of instantaneous distance \(r\) from line charge, is proportional to

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is \((A)\) directly proportional to the length of the potentiometer wire \((B)\) directly proportional to the potential gradient of the wire \((C)\) inversely proportional to the potential gradient of the wire \((D)\) inversely proportional to the length of the potentiometer wire Choose the correct option for the above statements:

The potential energy of a particle of mass \(4\,kg\) in motion along the \(x\)-axis is given by \(U =4(1-\cos 4 x )\,J\). The time period of the particle for small oscillation \((\sin \theta \simeq \theta)\) is \(\left(\frac{\pi}{ K }\right)\,s\). The value of \(K\) is .......

A smooth wire of length \(2\pi r\) is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed \(\omega\) about the vertical diameter \(AB\), as shown in figure, the bead is at rest with respect to the circular ring at position \(P\) as shown. Then the value of \(\omega^2\) is equal to