The given circuit works as :

The measured value of the length of a simple pendulum is \(20 \mathrm{~cm}\) with \(2 \mathrm{~mm}\) accuracy. The time for \(50\) oscillations was measured to be \(40\) seconds with \(1\) second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \(\mathrm{N} \%\). The value of \(\mathrm{N}\) is _______.

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is \(30^{\circ}\) in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is _______ \(\mu \mathrm{m}\).

The four arms of a Wheatstone bridge have resistances as shown in the figure. A  galvanometer of \(15\, \Omega\) resistance is connected across \(BD\). Calculate the current through the galvanometer when a potential difference of \(10\, V\) is maintained across \(AC.\)

A radioactive nucleus can decay by two different processes. Half-life for the first process is \(3.0\, hours\) while it is \(4.5\, hours\) for the second process. The effective half- life of the nucleus will be \(.........\,hours.\)

A system consists of two identical spheres each of mass \(1.5\, {kg}\) and radius \(50\, {cm}\) at the end of light rod. The distance between the centres of the two spheres is \(5\, {m}\). What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint ? (in \({kgm}^{2}\))

At the centre of a fixed large circular coil of radius \(R\), a much smaller circular coil of radius \(r\) is placed. The two coils are concentric and are in the same plane. The larger coil carries a current \(I\). The smaller coil is set to rotate with a constant angular velocity \(\omega \) about an axis along their common diameter. Calculate the \(emf\) induced in the smaller coil after a time \(t\) of its start of rotation

A circular disc of radius \(b\) has a hole of radius \(a\) at its centre (see figure). If the mass per unit area of the disc varies as \(\left( {\frac{{{\sigma _0}}}{r}} \right)\), then the radius of gyration of the disc about its axis passing through the centre is

The value of unknown resistance \((x)\) for which the potential difference between \(B\) and \(D\) will be zero in the arrangement shown, is _______.

A wire of resistance \(R\) is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points \(A\) and \(B\) is \(R / n\). The value of \(n\) is :

\(M\) grams of steam at \(100^{\circ} \mathrm{C}\) is mixed with \(200\; \mathrm{g}\) of ice at its melting point in a thermally insulated container. If it produces liquid water at \(40^{\circ} \mathrm{C}\) [heat of vaporization of water is \(540 \;cal/\mathrm{g}\) and heat of fusion of ice is \(80 \;\text { cal/g }]\) the value of \(\mathrm{M}\) is