The amplitude of a damped oscillator decreases to \(0.9\) times its original magnitude in \(5\ s\). In another \(10\ s\) it will decrease to \(\alpha \) times its original magnitude, where  \(\alpha \) equals

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass \(4\;kg\). (The coordinates of the same are shown in figure) are

The de-Broglie wavelength associated with a particle of mass \(m\) and energy \(E\) is \(\mathrm{h} / \sqrt{2 m E}\) The dimensional formula for Planck's constant is _______.

Two electrons each are fixed at a distance \('2d'\). A third charge proton placed at the midpoint is displaced slightly by a distance \(x ( x << d )\) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : \(( m =\) mass of charged particle)

Consider two charged metallic spheres \(S_{1}\) and \(\mathrm{S}_{2}\) of radii \(\mathrm{R}_{1}\) and \(\mathrm{R}_{2},\) respectively. The electric \(\left.\text { fields }\left.\mathrm{E}_{1} \text { (on } \mathrm{S}_{1}\right) \text { and } \mathrm{E}_{2} \text { (on } \mathrm{S}_{2}\right)\) on their surfaces are such that \(\mathrm{E}_{1} / \mathrm{E}_{2}=\mathrm{R}_{1} / \mathrm{R}_{2} .\) Then the ratio \(\left.\mathrm{V}_{1}\left(\mathrm{on}\; \mathrm{S}_{1}\right) / \mathrm{V}_{2} \text { (on } \mathrm{S}_{2}\right)\) of the electrostatic potentials on each sphere is 

Two point charges \(8 \, \mu C\) and \(-2 \, \mu C\) are located at \(x = 2\) cm and \(x = 4\) cm, respectively on the \(x\)-axis. The ratio of electric flux due to these charges through two spheres of radii \(3\) cm and \(5\) cm with their centers at the origin is _______.

A steel wire having a radius of \(2.0\, mm\), carrying a load of \(4\, kg\), is hanging from a ceiling. Given that \(g = 3.1\pi \,m{s^{ - 2}}\) , what will be the tensile stress that would be developed in the wire?

The surface tension of soap solution is \(3.5 \times 10^{-2}\,Nm ^{-1}\). The amount of work done required to increase the radius of soap bubble from \(10\,cm\) to \(20\,cm\) is \(.....\times 10^{-4}\,J\)

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because
A. The size of gold nucleus is very small as compared to the size of gold atom.
B. Alpha particle and gold nucleus have equal charge.
C. The impact parameter is minimum for a few alpha particles.
D. A few alpha particles have very high kinetic energy.
E. Only a few alpha particles undergo head-on collision with the nuclei.
Choose the correct answer from the options given below:

The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is _______.