An \(AC\) source rated \(220\, V , 50\, Hz\) is connected to a resistor. The time taken by the current to change from its maximum to the rms value is

A \(1 \mathrm{~kg}\) mass is suspended from the ceiling by a rope of length \(4 \mathrm{~m}\). A horizontal force ' \(F\) ' is applied at the mid point of the rope so that the rope makes an angle of \(45^{\circ}\) with respect to the vertical axis as shown in figure. The magnitude of \(F\) is _______.

Two planets \(A\) and \(B\) of equal mass are having their period of revolutions \(T_{A}\) and \(T_{B}\) such that \(T_{A}=2 T_{B}\). These planets are revolving in the circular orbits of radii \(I_{A}\) and \(I_{B}\) respectively. Which out of the following would be the correct relationship of their orbits?

A plane polarized monochromatic \(EM\) wave is travelling a vacuum along \(z\) direction such that at \(t\, = t_1\) it is found that the electric field is zero at a spatial point \(z_1\) . The next zero that occurs in its neighbourhood is at \(z_2\). The frequency of the electromagnetic wave is:

A block of mass \(m\), lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant \(k\). The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force \(F\), the maximum speed of the block is

A simple harmonic oscillator has an amplitude \(A\) and time period \(6 \pi\) second. Assuming the oscillation starts from its mean position, the time required by it to travel from \(x=A\) to \(x=\frac{\sqrt{3}}{2} A\) will be \(\frac{\pi}{x}\) s, where \(x=\) _______.

For ac circuit shown in figure, \(\mathrm{R}=100 \mathrm{k} \Omega\) and \(\mathrm{C}=100 \mathrm{pF}\) and the phase difference between \(\mathrm{V}_{\text {in }}\) and \(\left(V_B-V_A\right)\) is \(90^{\circ}\). The input signal frequency is \(10^x \mathrm{rad} / \mathrm{sec}\), where ' 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, \(\left.\mathrm{G}=10^{10} \mathrm{~N} / \mathrm{m}^2\right)\)

Match List \(- I\) (Fundamental Experiment) with List \(- II\) (its conclusion) and select the correct option from the choices given below the list \(\begin{array}{|||} \hline List\,\,-1  & List\,\,-II\,\,  \\ \hline a\,\,Franck-Hertz\,\,Experiment & i\,\,Particle\,\,nature\,\,of\,\,light \\ \hline b\,\,Photo\,\,-electric\,\,Experiment & ii\,\,Discrete\,\,energy \,\, levels\,\,of\,\,atom \\ \hline c\,\,Davison-Germer\,\,Experiment & iii\,\,Wave\,\,nature\,\,of\,\,electron \\ \hline  & iv\,\,Structure\,\,of\,\,atom  \\ \hline \end{array}\)

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A:\) Diffusion current in a \(p-n\) junction is greater than the drift current in magnitude if the junction is forward biased. Reason \(R:\) Diffusion current in a \(p-n\) junction is from the \(n\)-side to the \(p\)-side if the junction is forward biased. In the light of the above statements, choose the most appropriate answer from the options given below

Sun light falls normally on a surface of area \(36\,cm ^{2}\) and exerts an average force of \(7.2 \times 10^{-9}\,N\) within a time period of \(20\) minutes. Considering a case of complete absorption, the energy flux of incident light is.