A cubical block of side \(30\,cm\)  is moving with  velocity \(2\,\,ms^{-1}\) on a smooth horizontal surface. The surface has a bump at a point \(O\) as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is

A particle is executing simple harmonic motion. Its amplitude is \(A\) and time period is \(5\) sec. The time required by it to move from \(x = A\) to \(x = \dfrac{A}{\sqrt{2}}\) is _______ sec.

The workdone by a gas molecule in an isolated system is given by, \(W =\alpha \beta^{2} e ^{-\frac{ x ^{2}}{\alpha kT }},\) where \(x\) is the displacement, \(k\) is the Boltzmann constant and \(T\) is the temperature, \(\alpha\) and \(\beta\) are constants. Then the dimension of \(\beta\) will be

A gas has \(n\) degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be.

A mixture of \(2\, moles\) of helium gas (atomic mass \(= 4\, u\)), and \(1\, mole\) of argon gas (atomic mass \(= 40\, u\)) is kept at \(300\, K\) in a container. The ratio of their rms speeds \(\left[ {\frac{{{V_{rms}}{\rm{(helium)}}}}{{{V_{rms}}{\rm{(argon)}}}}} \right]\), is close to

Given below are two statements: Statement \(I:\) Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement \(II:\) Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light. In the light of above statements, choose the correct answer from the options given below:

When an external resistance of \(5\ \Omega\) is connected across terminals of a cell, a current of \(0.25\text{ A}\) flows through it. When the \(5\ \Omega\) resistor is replaced by a \(2\ \Omega\) resistor, a current of \(0.5\text{ A}\) flows through it. The internal resistance of the cell is _______ \(\Omega\).

A hydrogen atom changes its state from \(n=3\) to \(\mathrm{n}=2\). Due to recoil, the percentage change in the wave length of emitted light is approximately \(1 \times 10^{-\mathrm{n}}\). The value of \(\mathrm{n}\) is _______. [Given \(\mathrm{Rhc}=13.6 \mathrm{eV}, \mathrm{hc}=1242 \mathrm{eV} \mathrm{nm}\), \(\mathrm{h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}\), mass of the hydrogen atom \(\left.=1.6 \times 10^{-27} \mathrm{~kg}\right]\)

In an adiabatic process, which of the following statements is true?

In a photoelectric experiment ultraviolet light of wavelength \(280\, {nm}\) is used with lithium cathode having work function \(\phi=2.5\, {eV}\). If the wavelength of incident light is switched to \(400\, {nm}\), find out the change in the stopping potential (in \({V}\)). \(\left({h}=6.63 \times 10^{-34}\, {J} \cdots\right.\), \(\left.{c}=3 \times 10^{8} \,{ms}^{-1}\right)\) 

The electric field in a region is given by \(\overrightarrow{ E }=\frac{2}{5} E _{0} \hat{ i }+\frac{3}{5} E _{0} \hat{ j }\) with \(E _{0}=4.0 \times 10^{3}\, \frac{ N }{ C } .\) The flux of this field through a rectangular surface area \(0.4 \,m ^{2}\) parallel to the \(Y - Z\) plane is ....... \(Nm ^{2} C ^{-1}\)

The plot given below is of the average power delivered to an \(LRC\) circuit versus frequency. The quality factor of the circuit is