In the electric network shown, when no current flows through the \(4\, \Omega \) resistor in the arm \(EB\), the potential difference between the points \(A\) and \(D\) will be ............... \(V\)

A parallel plate capacitor with plate separation \(5\) \(\mathrm{mm}\) is charged up by a battery. It is found that on introducing a dielectric sheet of thickness \(2 \mathrm{~mm}\), while keeping the battery connections intact, the capacitor draws \(25 \%\) more charge from the battery than before. The dielectric constant of the sheet is _______.

Identify the physical quantity that cannot be measured using spherometer :

Two conducting circular loops \(A \) and \(B\) are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is _______.

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of \(100 \mathrm{~cm}^2\) with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density \(1.5 \times 10^3 \mathrm{~kg} / \mathrm{m}^3\). What force one needs to apply on the hinged door so that it does not get opened ?
(Acceleration due to gravity \(=10 \mathrm{~m} / \mathrm{s}^2\))

A system of three charges are placed as shown in the figure. If  \(D > > d,\) the potential energy of the system is best given \(b\)

Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E . The energy stored in B , when spring constants \(k _{ A }, k _{ B }\) of A and \(B\), respectively satisfy the relation \(4 k _{ A }=3 k _{ B }\), is :

In the given circuit ' \(a\) ' is an arbitrary constant. The value of \(m\) for which the equivalent circuit resistance is minimum, will be \(\sqrt{\frac{ x }{2}}\). The value of \(x\) is ...........

In the given figure, two wheels \(P\) and \(Q\) are connected by a belt \(B\). The radius of \(P\) is three times as that of \(Q\). In case of same rotational kinetic energy, the ratio of rotational inertias \(\left(\frac{{I}_{1}}{{I}_{2}}\right)\) will be \({x}: 1\). The value of \({x}\) will be \(.....\, .\)

A proton and an \(\alpha\)-particle are accelerated from rest by \(2\,V\) and \(4\,V\) potentials, respectively. The ratio of their de-Broglie wavelength is:

Temperature difference of \(120\,^oC\) is maintained between two ends of a uniform rod \(AB\) of length \(2L\). Another bent rod \(PQ\), of same cross-section as \(AB\) and length \(\frac{{3L}}{2}\),  is connected across \(AB\) (See figure). In steady state, temperature difference between \(P\) and \(Q\) will be close to .......... \(^oC\)

As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is :

A particle executes simple harmonic motion with an amplitude of \(4 \mathrm{~cm}\). At the mean position, velocity of the particle is \(10 \mathrm{~cm} / \mathrm{s}\). The distance of the particle from the mean position when its speed becomes \(5 \mathrm{~cm} / \mathrm{s}\) is \(\sqrt{\alpha} \mathrm{cm}\), where \(\alpha=\)____________.