A ray of light entering from air into a denser medium of refractive index \(\frac{4}{3}\), as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum, value of angle \(\theta\) should be equal to -

Calculate the value of mean free path \((\lambda)\) for oxygen molecules at temperature \(27^{\circ}\, C\) and pressure \(1.01 \times 10^{5} \,Pa\). Assume the molecular diameter \(0.3 \,nm\) and the gas is ideal. \(\left( k =1.38 \times 10^{-23}\, J\,K ^{-1}\right)\) (in \(nm\))

The magnetic field existing in a region is given by \(\overrightarrow{\mathrm{B}}=0.2(1+2 \mathrm{x}) \hat{\mathrm{k} T}\). A square loop of edge \(50 \mathrm{~cm}\) carrying \(0.5 \mathrm{~A}\) current is placed in \(x-y\) plane with its edges parallel to the \(x-y\) axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is___________ \(\mathrm{mN}\).

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is

Statement \(I:\) If three forces \(\vec{F}_{1}, \vec{F}_{2}\) and \(\vec{F}_{3}\) are represented by three sides of a triangle and \(\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}\), then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement \(II:\) A triangle made up of three forces \(\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}\) and \(\overrightarrow{{F}}_{3}\) as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below:

A particle of mass \(1 \,{mg}\) and charge \(q\) is lying at the mid-point of two stationary particles kept at a distance \('2 \,{m}^{\prime}\) when each is carrying same charge \('q'.\) If the free charged particle is displaced from its equilibrium position through distance \('x'\) \((x\,< \,1\, {m})\). The particle executes \(SHM.\) Its angular frequency of oscillation will be \(....\,\times 10^{8}\, {rad} / {s}\) if \({q}^{2}=10\, {C}^{2}\)

A \(90 \mathrm{~kg}\) body placed at \(2 \mathrm{R}\) distance from surface of earth experiences gravitational pull of _______. ( \(\mathrm{R}=\) Radius of earth, \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

The refractive index of a prism with apex angle \(A\) is \(\cot A / 2\). The angle of minimum deviation is _______.

Which of the following curves possibly represent one-dimensional motion of a particle?




Choose the correct answer from the options given below :