A parallel plate capacitor with plates of area \(1\,m^2\) each, are at a separation of \(0.1\,m.\) If the electric field between the plates is \(100\,N/C,\) the magnitude of charge on each plate

A capacitor \(C _{1}\) of capacitance \(5\,\mu F\) is charged to a potential of \(30\,V\) using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor \(C _{2}\) of capacitance \(10\,\mu F\) as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor \(C _{2}\) is________ \(\mu C\)

An ideal gas initially at \(0^{\circ} \mathrm{C}\) temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is \(3 / 2\), the change in temperature due to the thermodynamic process is _____ K.

As per the given circuit, the value of current through the battery will be \(\dots \; A\).

A particle is moving with constant speed in a circular path. When the particle turns by an angle \(90^{\circ}\), the ratio of instantaneous velocity to its average velocity is \(\pi: x \sqrt{2}\). The value of \(x\) will be \(.........\)

A particular hydrogen - like ion emits the radiation of frequency \(3 \times 10^{15} \mathrm{~Hz}\) when it makes transition from \(n=2\) to \(n=1\). The frequency of radiation emitted in transition from \(n=3\) to \(n=1\) is \(\frac{x}{9} \times 10^{15} \mathrm{~Hz}\), when \(x=\) = _____.

A force is represented by \(\mathrm{F}=a \mathrm{x}^2+\mathrm{bt}^{1 / 2}\). Where \(\mathrm{x}=\) distance and \(\mathrm{t}=\) time. The dimensions of \(\mathrm{b}^2 / \mathrm{a}\) are _______.

Car \(B\) overtakes another car \(A\) at a relative speed of \(40\, ms^{-1}\). How fast will the image of car \({B}\) appear to move in the mirror of focal length \(10\, cm\) fitted in car \({A}\), when the car \({B}\) is \(1.9\, m\) away from the car \({A}\) ? (In \(ms^{-1}\))

The time period of a simple pendulum is given by \(T =2 \pi \sqrt{\frac{\ell}{ g }}\). The measured value of the length of pendulum is \(10\, cm\) known to a \(1\, mm\) accuracy. The time for \(200\) oscillations of the pendulum is found to be \(100\) second using a clock of \(1s\) resolution. The percentage accuracy in the determination of \('g'\) using this pendulum is \('x'\). The value of \('x'\) to the nearest integer is ...........\(\%\)

Assume that an electric field \(\vec E = 30{x^2}\hat i\) exists in space. Then the potential difference \(V_A-V_O\) where \(V_O\) is the potential at the origin and \(V_A\) the potential at \(x = 2\ m\) is....\(V\)

The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length \(L ( R < L )\) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M ) :

An antenna is placed in a dielectric medium of dielectric constant \(6.25\). If the maximum size of that antenna is \(5.0\, mm\). it can radiate a signal of minimum frequency of \(GHz .\) (Given \(\mu_{ r }=1\) for dielectric medium)

Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is \(x: y .\) The value of \(x\) is ...... .