The electric current in the circuit is given as \(i=i_{ o }(t / T)\). The r.m.s current for the period \(t=0\) to \(t=T\) is ___________

An electric dipole of mass m, charge q, and length \(l\) is placed in a uniform electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

A parallel plate capacitor with air between the plate has a capacitance of \(15 pF\). The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant \(3.5.\) Then the capacitance becomes \(\frac{ x }{4}\,pF\).The value of \(x\) is \(............\)

When one light ray is reflected from a plane mirror with \(30^{\circ}\) angle of reflection, the angle of deviation of the ray after reflection is \(.....^{\circ}\)

The figure represents the momentum time \((p-t)\) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ? If \(\left(t_3-t_2\right) < t_1\)

With rise in temperature, the Young's modulus of elasticity _______.

A Carnot engine absorbs \(1000\,J\) of heat energy from a reservoir at \(127\,^oC\) and rejects \(600\,J\) of heat energy during each cycle. The efficiency of engine and temperature of sink will be

What will be the projection of vector \(A=\hat{i}+\hat{j}+\hat{k}\) on vector \(\vec{B}=\hat{i}+\hat{j}\).

The planet Mars has two moons, if one of them has a period \(7\, hours,\, 30\, minutes\) and an orbital radius of \(9.0 \times 10^{3}\, {km} .\) Find the mass of Mars. \(\left\{\operatorname{Given} \frac{4 \pi^{2}}{G}=6 \times 10^{11} {N}^{-1} {m}^{-2} {kg}^{2}\right\}\)

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :

Three identical particle \(A , B\) and \(C\) of mass \(100\, kg\) each are placed in a straight line with \(AB = BC =13 \,m\). The gravitational force on a fourth particle \(P\) of the same mass is \(F\), when placed at a distance \(13 \,m\) from the particle \(B\) on the perpendicular bisector of the line \(AC\). The value of \(F\) will be approximately\(....G\)

A vector \(\vec A \) is rotated by a small angle \(\Delta \theta\) radian \(( \Delta \theta << 1)\) to get a new vector \(\vec B\) In that case \(\left| {\vec B - \vec A} \right|\) is

A \(2\,mW\) laser operates at a wavelength of \(500\,nm.\) The number of photons that will be emitted per second is [Given Planck’s constant \(h = 6.6 \times 10^{-34}\,Js,\) speed of light \(c = 3.0\times 10^8\,m/s\) ]