If the electric potential at any point \((x, y, z) \,m\) in space is given by \(V =3 x ^{2}\) volt. The electric field at the point \((1,0,3) \,m\) will be ............

Find the magnetic field at the point \(P\) in figure. The curved portion is a semicircle connected to two long straight wires.

In a Young's double slit experiment two slits are separated by \(2\, mm\) and the screen is placed one meter away. When a light of wavelength \(500 \,nm\) is used, the fringe separation will be ........ \(mm\)

A batsman hits back a ball of mass \(0.4 \; kg\) straight in the direction of the bowler without changing its initial speed of \(15 \; ms ^{-1}\). The impulse imparted to the ball is \(\dots \; Ns\)

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of \(\Delta Q : \Delta U : \Delta W\) is _______.

The temperature dependence of resistances of \(Cu\) and undoped \(Si\) in the temperature range \(300-400\;K\), is best described by

Consider a sphere of radius \(\mathrm{R}\) which carries a uniform charge density \(\rho .\) If a sphere of radius \(\frac{\mathrm{R}}{2}\) is carved out of it, as shown, the ratio \(\frac{\left|\overrightarrow{\mathrm{E}}_{\mathrm{A}}\right|}{\left|\overrightarrow{\mathrm{E}}_{\mathrm{B}}\right|}\) of magnitude of electric field \(\overrightarrow{\mathrm{E}}_{\mathrm{A}}\) and \(\overrightarrow{\mathrm{E}}_{\mathrm{B}}\) respectively, at points \(\mathrm{A}\) and \(\mathrm{B}\) due to the remaining portion is

A uniform sphere of weight \(W\) and radius \(5\, cm\) is being held by a string as shown in the figure. The tension in the string will be

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to \(\operatorname{arc} \mathrm{AB}\) to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?

The following logic gate is equivalent to

The equation of motion of a particle is given by \(x = a \sin\left(50t + \dfrac{\pi}{3}\right)\) cm. The particle will come to rest at time \(t_1\) and it will have zero acceleration at time \(t_2\). The \(t_1\) and \(t_2\) respectively are _______.