Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is \(1: 4\), then \(A.\) The \(r.m.s\). velocity of gas molecules in two vessels will be the same. \(B.\) The ratio of pressure in these vessels will be \(1: 4\) \(C.\) The ratio of pressure will be \(1: 1\) \(D.\) The \(r.m.s.\) velocity of gas molecules in two vessels will be in the ratio of \(1: 4\)

Two identical solid spheres each of mass \(2\,kg\) and radii \(10\,cm\) are fixed at the ends of a light rod. The separation between the centres of the spheres is \(40\,cm\). The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is \(........... \times 10^{-3}\,kg - m ^2\)

The elongation of a wire on the surface of the earth is \(10^{-4} \; m\). The same wire of same dimensions is elongated by \(6 \times 10^{-5} \; m\) on another planet. The acceleration due to gravity on the planet will be \(\dots \; ms ^{-2}\). (Take acceleration due to gravity on the surface of earth \(=10 \; m / s ^{-2}\) )

Consider a moving coil galvanomenter (MCG):
A. The torsional constant in moving coil galvanometer has dimentions \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.
C. If we increase number of turns \((\mathrm{N})\) to its double \((2 \mathrm{~N})\), then the voltage sensitivity doubles.
D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.
E. Current sensitivity of MCG depends inversely on number of turns of coil.
Choose the correct answer from the options given below:

The electric field of light wave is given as \(\vec E\, = \,{10^{ - 3}}\,\cos \,\,\left( {\frac{{2\pi x}}{{5 \times {{10}^{ - 7}}}} - 2\pi  \times 6 \times {{10}^{14}}t} \right)\hat x\frac{N}{C}\). This light falls on a metal plate of work function \(2\,eV.\) The stopping potential of the photoelectrons is ................ \(V\)

Three masses \(m,\,2\,m\) and \(3\,m\) are moving in \(x-y\) plane with speed \(3\,u,\,2\,u\,\) and \(u\) respectively as shown in figure. The three masses collide at the same point at \(P\) and stick together. The velocity of resulting mass will be

A proton and an electron have the same de Broglie wavelength. If \(K_p\) and \(K_e\) be the kinetic energies of proton and electron respectively. Then choose the correct relation :

Given below are two statements. Statement \(I\) : Electric potential is constant within and at the surface of each conductor. Statement \(II\) : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options give below.

The motion of a mass on a spring, with spring constant \({K}\) is as shown in figure. The equation of motion is given by \(x(t)= A sin \omega t+ Bcos\omega t\) with \(\omega=\sqrt{\frac{K}{m}}\) Suppose that at time \(t=0\), the position of mass is \(x(0)\) and velocity \(v(0)\), then its displacement can also be represented as \(x(t)=C \cos (\omega t-\phi)\), where \(C\) and \(\phi\) are