An electric field \(\vec E\, = (25 \hat i + 30 \hat j)\,NC^{-1}\) exists in a region of space. If the potential at the origin is taken to be zero then the potential at \(x\, = 2\, m, y\, = 2\, m\) is......\(volt\)

A block of mass \(200\, g\) is kept stationary on a smooth inclined plane by applying a minimum horizontal force \(F =\sqrt{ x }N\) as shown in figure. The value of \(x =.....\)

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

Two radioactive substances \(A\) and \(B\) have decay constants \(5\lambda \) and \(\lambda \) respectively. At \(t = 0\), a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become \((\frac {1}{e})^2\) will be

In an \(LCR\) series circuit, an inductor \(30 \,{mH}\) and a resistor \(1 \, \Omega\) are connected to an \(AC\) source of angular frequency \(300 \, {rad} / {s}\). The value of capacitance for which, the current leads the voltage by \(45^{\circ}\) is \(\frac{1}{x} \times 10^{-3} \, {F}\). Then the value of \(x\) is ..... .

A bead \(P\) sliding on a frictionless semi-circular string \((A C B)\) and it is at point \(S\) at \(t =0\) and at this instant the horizontal component of its velocity is \(v\). Another bead \(Q\) of the same mass as \(P\) is ejected from point \(A\) at \(t =0\) along the horizontal string \(A B\), with the speed \(v\), friction between the beads and the respective strings may be neglected in both cases. Let \(t_p\) and \(t_Q\) be the respective times taken by beads \(P\) and \(Q\) to reach the point \(B\), then the relation between \(t_p\) and \(t_Q\) is

Two wires \(A\) and \(B\) are carrying currents \(I_1\) and \(I_2\) as shown in the figure. The separation between them is \(d\). A third wire \(C\) carrying a current \(I\) is to be kept parallel to them at a distance \(x\) from \(A\) such that the net force acting on it is zero. The possible values of \(x\) are

An \(EM\) wave propagating in \(x\)-direction has a wavelength of \(8\,mm\). The electric field vibrating \(y\) direction has maximum magnitude of \(60\,Vm ^{-1}\). Choose the correct equations for electric and magnetic fields if the \(EM\) wave is propagating in vacuum

In finding the electric field using Gauss Law the formula \(|\overrightarrow{\mathrm{E}}|=\frac{q_{\mathrm{enc}}}{\varepsilon_{0}|\mathrm{A}|}\) is applicable. In the formula \(\varepsilon_{0}\) is permittivity of free space, \(A\) is the area of Gaussian surface and \(q_{enc}\) is charge enclosed by the Gaussian surface. The equation can be used in which of the following situation?

A parallel plate capacitor with plate area \(A\) and plate separation \(d\) is filled with a dielectric material of dielectric constant \(K =4\). The thickness of the dielectric material is \(x\), where \(x < d\). Let \(C_1\) and \(C_2\) be the capacitance of the system for \(x =\frac{1}{3} d\) and \(x =\frac{2 d }{3}\), respectively. If \(C _1=2 \mu F\) the value of \(C _2\) is \(........... \mu F\)

A uniform chain of length \(3\, meter\) and mass \(3\, {kg}\) overhangs a smooth table with \(2\, meter\) laying on the table. If \(k\) is the kinetic energy of the chain in joule as it completely slips off the table, then the value of \({k}\) is (Take \(\left.g=10\, {m} / {s}^{2}\right)\)

On a linear temperature scale \(Y\), water freezes at \(- 160^o\, Y\) and boils at \(- 50^o\, Y\). On this \(Y\) scale , a temperature of \(340\, K\) would be read as........ \(^oY\)  ( water freezes at \(273\, K\) and boils at \(373\, K\))