A transverse wave is represented by \(y=2 \sin\) \((\omega t - kx ) cm\). The value of wavelength (in \(cm\) ) for which the wave velocity becomes equal to the maximum particle velocity, will be.

If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be \(...\%\)

Given below are two statements:
Statement I: The hot water flows faster than cold water.
Statement II: Soap water has higher surface tension as compared to fresh water.
In the light above statements, choose the correct answer from the options given below.

Two ions of masses \(4 \,{amu}\) and \(16\, amu\) have charges \(+2 {e}\) and \(+3 {e}\) respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :

If the potential energy between two molecules is given by \(U =\frac{-A }{ r ^{6}}+\frac{ B }{ r ^{12}},\) then at equilibrium, separation between molecules, and the potential energy are

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A :\) Moment of inertia of a circular disc of mass \('M'\) and radius \('R'\) about \(X, Y\) axes (passing through its plane) and \(Z-\)axis which is perpendicular to its plane were found to be \(I_{x}, I_{y}\) and \({I}_{z}\) respectively. The respective radii of gyration about all the three axes will be the same. Reason \(R\) : A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below :

A particle performs simple harmonic motion with a period of \(2\) second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is \(\frac{1}{ a } s .\) The value of \('a'\) to the nearest integer is.........

Which of the following statement is not true about stopping potential \(\left(\mathrm{V}_0\right)\)?

The temperature of \(3.00\, {mol}\) of an ideal diatomic gas is increased by \(40.0^{\circ} {C}\) without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of workdone by the gas is \(\frac{{x}}{10} .\) Then the value of \({x}\) (round off to the nearest integer) is ..... . \(\left(\right.\) Given \(\left.{R}=8.31\, {J} {mol}^{-1} {K}^{-1}\right)\)

Consider the following statements : \(A.\) Atoms of each element emit characterstics spectrum. \(B.\) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit. \(C.\) The density of nuclear matter depends on the size of the nucleus. \(D.\) A free neutron is stable but a free proton decay is possible. \(E.\) Radioactivity is an indication of the instability of nuclei. Choose the correct answer from the options given below 

A small object at rest, absorbs a light pulse of power \(20\,mW\) and duration \(300\,ns\). Assuming speed of light as \(3 \times 10^8\,m / s\). the momentum of the object becomes equal to \(.........\times 10^{-17} kg\,m / s\)

A parallel plate capacitor has plate of length \('l',\) width \('w'\) and separation of plates is \('d'.\) It is connected to a battery of emf \(V\). A dielectric slab of the same thickness '\(d\)' and of dielectric constant \(k =4\) is being inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored\(?\)