In an experiment to find acceleration due to gravity \((g)\) using simple pendulum, time period of \(0.5\,s\) is measured from time of \(100\) oscillation with a watch of \(1\;s\) resolution. If measured value of length is \(10\; cm\) known to \(1\; mm\) accuracy. The accuracy in the determination of \(g\) is found to be \(x \%\). The value of \(x\) is

Two particles \(\mathrm{X}\) and \(\mathrm{Y}\) having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radius \(R_1\) and \(R_2\) respectively. The mass ratio of \(\mathrm{X}\) and \(\mathrm{Y}\) is _______.

As shown in the figure, two infinitely long, identical wires are bent by \(90^o\) and placed in such a way that the segments \(LP\) and \(QM\) are along the \(x-\) axis, while segments \(PS\) and \(QN\) are parallel to the \(y-\) axis. If \(OP = OQ = 4\, cm\), and the magnitude of the magnetic field at \(O\) is \(10^{-4}\, T\), and the two wires carry equal current (see figure), the magnitude of the current in each wire and the direction of the magnetic field at \(O\) will be \((\mu_ 0 = 4\pi \times10^{-7}\, NA^{-2})\)

Space between two concentric conducting spheres of radii \(a\) and \(b (b > a)\) is filled with \(a\) medium of resistivity \(\rho \). The resistance between the two spheres will be

As per given figure, a weightless pulley \(P\) is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if \(g=\) \(10\,m / s ^2\) )

A uniform metallic wire is elongated by \(0.04\, m\) when subjected to a linear force \(F\). The elongation, if its length and diameter is doubled and subjected to the same force will be ..... \(cm .\)

In a series \(L-C-R\) circuit, \(C = 10^{-11}\,Farad.\) \(L = 10^{-5}\,Henry\) and \(R =100\,Ohm.\) when a constant \(D.C.\) voltage \(E\) is applied to the circuit, the capacitor acquires a charge \(10^{-9}\,C\) .The \(D.C.\) source is replaced by a sinusoidal voltage source in which the peak voltage \(E_0\) is equal to the constant \(D.C.\) voltage \(E.\) At resonance the peak value of the charge acquired by the capacitor will be

The half-life of a radioactive nucleus is \(5\) years, The fraction of the original sample that would decay in \(15\) years is

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.

For which of the following particles will it be most difficult to experimentally verify the deBroglie relationship?

A train is moving on a straight track with speed \(20\ ms^{-1}\). It is blowing its whistle at the frequency of \(1000\ Hz\). The percentage change in the frequency heard by a person standing near the track as the train passes him is ( speed of sound \(=320\) \(ms^{-1}\) ) close to .... \(\%\)