A capacitor C is first charged fully with potential difference of \( V_{0} \) and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In time t, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is

The displacement of simple harmonic oscillator after \(3\) seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is \(\dots \; s\)

Ten charges are placed on the circumference of a circle of radius \(R\) with constant angular separation between successive charges. Alternate charges \(1,3,5,7,9\) have charge \((+q)\) each, while \(2,4,6,8,10\) have charge \((-q)\) each. The potential \(V\) and the electric field \(E\) at the centre of the circle are respectively (Take \(V =0\) at infinity \()\)

Young's modulus is determined by the equation given by \(\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}\) where \(\mathrm{M}\) is the mass and \(\ell\) is the extension of wre used in the experiment. Now error in Young modules \((\mathrm{Y})\) is estimated by taking data from \(M-\ell\) plot in graph paper. The smallest scale divisions are \(5 \mathrm{~g}\) and \(0.02\) \(\mathrm{cm}\) along load axis and extension axis respectively. If the value of \(M\) and \(\ell\) are \(500 \mathrm{~g}\) and \(2 \mathrm{~cm}\) respectively then percentage error of \(\mathrm{Y}\) is _______.

The momentum of an electron revolving in \(n ^{\text {th }}\) orbit is given by: (Symbols have their usual meanings)

A block of metal weighing \(2 \,kg\) is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of \(1 \,kgs ^{-1}\) and at a speed of \(10 \,ms ^{-1}\). Then, the initial acceleration of the block, in \(ms ^{-2}\), will be .................

A circular disc of mass \(M\) and radius \(R\) is rotating about its axis with angular speed \(\omega_{1}\) If another stationary disc having radius \(\frac{ R }{2}\) and same mass \(M\) is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed \(\omega_{2}\). The energy lost in the process is \(p \%\) of the initial energy. Value of \(p\) is

The energy stored in the electric field produced by a metal sphere is \(4.5\, J\). lf the sphere contains \(4\,\mu C\) charge, its radius will be.......\(mm\) : [Take : \(\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N - {m^2}\,/{C^2}\, ]\)

For \(z=a^{2} x^{3} y^{\frac{1}{2}}\), where \(a\) is a constant. If percentage error in measurement of \(x\) and \(y\) are \(4 \%\) and \(12 \%\), respectively, then the percentage error for \(z\) will be \(%\)

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

In a Young's double slit experiment, an angular width of the fringe is \(0.35^{\circ}\) on a screen placed at \(2\,m\) away for particular wavelength of \(450\,nm\). The angular width of the fringe, when whole system is immersed in a medium of refractive index \(7 / 5\), is \(\frac{1}{\alpha}\). The value of \(\alpha\) is ..............