In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative \(z\)-axis and magnetic field is along the positive \(x\)-axis. Then the direction of propagation of electromagnetic wave is

One end of a metal wire is fixed to a ceiling and a load of \(2 \mathrm{~kg}\) hangs from the other end. A similar wire is attached to the bottom of the load and another load of \(1 \mathrm{~kg}\) hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be _______. [Area of cross section of wire \(=0.005 \mathrm{~cm}^2\), \(\mathrm{Y}=2 \times 10^{11}\  \mathrm{Nm}^{-2}\) and \(\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]\)

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : When a body is projected at an angle \(45^{\circ}\), it's range is maximum. Reason \(R\) : For maximum range, the value of \(\sin 2 \theta\) should be equal to one. In the light of the above statements, choose the correct answer from the options given below :

A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with 10 th bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same 10th bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660 nm would be _________ mm .

A simple harmonic oscillator of angular frequency \(2\,rad\,s^{-1}\) is acted upon by an external force \(F = sin\,t\,N .\) If the oscillator is at rest in its equilibrium position at \(t = 0,\) its position at later times is proportional to

Electric potential at a point \(P\) due to a point charge of \(5 \times 10^{-9}\; C\) is \(50 \;V\). The distance of \(P\) from the point charge is ......... \(cm\) (Assume, \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^{+9}\; Nm ^2 C ^{-2}\))

An ice cube of dimensions \(60\,cm \times 50\,cm \times 20\,cm\) is placed in an insulation box of wall thickness \(1\,cm\). The box keeping the ice cube at \(0^{\circ}\,C\) of temperature is brought to a room of temperature \(40^{\circ}\,C\). The rate of melting of ice is approximately. (Latent heat of fusion of ice is \(3.4 \times 10^{5}\,J\,kg ^{-1}\) and thermal conducting of insulation wall is \(0.05\,Wm ^{-10} C ^{-1}\) )

Three charges \(Q, +q\) and \(+q\) are placed at the vertices of a right -angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of \(Q\) is

For equal point charges \(Q\) each are placed in the \(xy\) plane at \((0, 2), (4, 2), (4, -2)\) and \((0, -2)\). The work required to put a fifth change \(Q\) at the origin of the coordinate system will be

The electric field in an electromagnetic wave is given as \(\vec{E}=20 \sin \omega\left(t-\frac{x}{c}\right) \vec{j} NC ^{-1}\) Where \(\omega\) and \(c\) are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of \(5 \times 10^{-4}\, m ^3\) will be \(.....\times 10^{-13}\,J\) (Given \(\varepsilon_0=8.85 \times 10^{-12}\,C ^2 / Nm ^2\) )