A parallel plate capacitor has plate area \(100\, m ^{2}\) and plate separation of \(10\, m\). The space between the plates is filled up to a thickness \(5\, m\) with a material of dielectric constant of \(10 .\) The resultant capacitance of the system is \('x'\) \(pF\). The value of \(\varepsilon_{0}=8.85 \times 10^{-12} F \cdot m ^{-1}\) The value of \('x'\) to the nearest integer is............

Given below are two statements: Statement \(I :\) Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an \(AC\) source, when resonance occurs Statement \(II :\) Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below :

The workdone in an adiabatic change in an ideal gas depends upon only :

In the circuit shown here, the voltage across \(L\) and \(C\) are respectively \(300\, V\) and \(400\, V\). The voltage \(E\) of the ac source is......\(Volt\)

Take the mean distance of the moon and the sun from the earth to be \(0.4 \times 10^6\,km\) and \(150 \times 10^6\,km\) respectively. Their masses are \(8 \times 10^{22}\, kg\) and \(2 \times 10^{30}\, kg\) respectively. The radius of the earth is \(6400\, km\). Let \(\Delta {F_1}\) be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and \(\Delta {F_2}\) be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to \(\frac{{\Delta {F_1}}}{{\Delta {F_2}}}\) is

The internal energy of air in \(4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}\) sized room at 1 atmospheric pressure will be _______ \(\times 10^6 \mathrm{~J}\). (Consider air as diatomic molecule)

A lift of mass \(1600\) kg is supported by thick iron wire. If the maximum stress which the wire can withstand is \(4 \times 10^8\) N/m\(^2\) and its radius is \(4\) mm, then maximum acceleration the lift can take is _______ m/s\(^2\). (take \(g = 10\) m/s\(^2\) and \(\pi = 3.14\))

A null point is found at \(200\,cm\) in potentiometer when cell in secondary circuit is shunted by \(5\,\Omega\). When a resistance of \(15\,\Omega\) is used for shunting null point moves to \(300\,cm\). The internal resistance of the cell is \(..............\,\Omega\).

Two identical solid spheres each of mass \(2\,kg\) and radii \(10\,cm\) are fixed at the ends of a light rod. The separation between the centres of the spheres is \(40\,cm\). The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is \(........... \times 10^{-3}\,kg - m ^2\)

A particle executes simple harmonic motion with an amplitude of \(5\, cm\). When the particle is at \(4\, cm\) from the mean position, the magnitude of its velocity is \(SI\,units\) is equal to that of its acceleration. Then, its periodic time in seconds is

Young's moduli of the material of wires \(A\) and \(B\) are in the ratio of \(1: 4\), while its area of cross sections are in the ratio of \(1: 3\). If the same amount of load is applied to both the wires, the amount of elongation produced in the wires \(A\) and \(B\) will be in the ratio of [Assume length of wires \(A\) and \(B\) are same]

A light wave travelling linearly in a medium of dielectric constant \(4,\) incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be (Given : relative permeability of medium \(\mu_{ s }=1)\)