What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of \(5\) times its mass? (Assume the collision to be head-on elastic collision)

The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross-section. Cross sectional areas at \(A\) is \(1.5\,cm ^2\), and \(B\) is \(25\,mm ^2\), if the speed of liquid at \(B\) is \(60\,cm / s\) then \(\left( P _{ A }- P _{ B }\right)\) is :(Given \(P _{ A }\) and \(P _{ B }\) are liquid pressures at \(A\) and \(B\) points.Density \(\rho=1000\,kg\,m ^{-3}\) \(A\) and \(B\) are on the axis of tube \(............\,Pa\)

The electrostatic potential due to an electric dipole at a distance '\(r\)' varies as _______.

If the \(rms\) speed of oxygen molecules at \(0^{\circ} {C}\) is \(160\; {m} / {s}\), find the rms speed of hydrogen molecules at \(0^{\circ} {C}\). (In \({m}/{s}\))

Two particles of equal mass \(\mathrm{m}\) have respective initial velocities \(u\hat{i}\) and \(u\left(\frac{\hat{\mathrm{i}}+ \hat{\mathrm{j}}}{2}\right) .\) They collide completely inelastically. The energy lost in the process is

If frequency of electromagnetic wave is \(60 \mathrm{MHz}\) and it travels in air along \(\mathrm{z}\) direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in \(\mathrm{m}\) ) is _______.

A particle of charge \(q\) and mass \(m\) is moving with a velocity \(-v \hat{ i }(v \neq 0)\) towards a large screen placed in the \(Y - Z\) plane at a distance \(d.\) If there is a magnetic field \(\overrightarrow{ B }= B _{0} \hat{ k },\) the minimum value of \(v\) for which the particle will not hit the screen is

The position of a particle as a function of time \(t\), is given by \(x\left( t \right) = at+ b{t^2} - c{t^3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

In an experiment for determination of refractive index of glass of a prism by \(i - \delta\) , plot it was found thata ray incident at angle \(35 ^o \), suffers a deviation of \(40 ^o \) and that it emerges at angle \(7 9 ^o \). In that case which of the following is closest to the maximum possible value of the refractive index?

From the photoelectric effect experiment, following observations are made. Identify which of these are correct \(A.\) The stopping potential depends only on the work function of the metal. \(B.\) The saturation current increases as the intensity of incident light increases. \(C.\) The maximum kinetic energy of a photo electron depends on the intensity of the incident light. \(D.\) Photoelectric effect can be explained using wave theory of light. Choose the correct answer from the options given below:

A convex lens is put \(10\, cm\) from a light source and it makes a sharp image on a screen, kept \(10\, cm\) from the lens. Now a glass block (refractive index \(1.5\)) of \(1.5\, cm\) thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance \(d\). Then \(d\) is

A parallel plate capacitor has plates of area \(A\) separated by distance \(d\) between them. It is filled with a dielectric which has a dielectric constant that varies as \(\mathrm{k}(\mathrm{x})=\mathrm{K}(1+\alpha \mathrm{x})\) where \(\mathrm{x}\) is the distance measured from one of the plates. If \((\alpha \text {d)}<<1,\) the total capacitance of the system is best given by the expression