Light wave traveling in air along \(x\)-direction is given by \(E _{ y }=540 \sin \pi \times 10^{4}( x - ct ) Vm ^{-1}\). Then, the peak value of magnetic field of wave will be \(\dots \times 10^{-7}\,T\) (Given \(c =3 \times 10^{8}\,ms ^{-1}\) )

An object of mass \(0.5\, {kg}\) is executing simple harmonic motion. Its amplitude is \(5\, {cm}\) and time period (T) is \(0.2\, {s} .\) What will be the potential energy of the object at an instant \(t=\frac{T}{4}\) s starting from mean position. Assume that the initial phase of the oscillation is zero. (In \({J}\))

\(1\,g\) of a liquid is converted to vapour at \(3 \times 10^5\,Pa\) pressure. If \(10 \%\) of the heat supplied is used for increasing the volume by \(1600\,cm ^3\) during this phase change, then the increase in internal energy in the process will be \(............\,J\)

A particle is moving in a circle of radius \(50 \mathrm{~cm}\) in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at \(t=0\) is \(4 \mathrm{~m} / \mathrm{s}\), the time taken to complete the first revolution will be \(\frac{1}{\alpha}\left[1-\mathrm{e}^{-2 \pi}\right] \mathrm{s}\), where \(\alpha=\) _______.

If e is the electronic charge, \(c\) is the speed of light in free space and \(h\) is Planck's constant, the quantity \(\frac{1}{4 \pi \varepsilon_{0}} \frac{| e |^{2}}{h c}\) has dimensions of .......

A loop ABCDA , carrying current \(\mathrm{I}=12 \mathrm{~A}\), is placed in a plane, consists of two semi-circular segments of radius \(R_1=6 \pi \mathrm{~m}\) and \(\mathrm{R}_2=4 \pi \mathrm{~m}\). The magnitude of the resultant magnetic field at center O is \(\mathrm{k} \times 10^{-7} \mathrm{~T}\). The value of k is ______ (Given \(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}\))

The speed of a longitudinal wave in a metallic bar is \(400~m/s.\) If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to ___________ \(m / s\).

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: