In the isothermal expansion of \(10\,g\) of gas from volume \(V\) to \(2V\) the work done by the gas is \(575\,J\). What is the root mean square speed of the molecules of the gas at that temperature ..... \(m/s\)?

A batsman hits back a ball of mass \(0.4 \; kg\) straight in the direction of the bowler without changing its initial speed of \(15 \; ms ^{-1}\). The impulse imparted to the ball is \(\dots \; Ns\)

Two resistors of \(100 \Omega\) each are connected in series with a 9 V battery. A voltmeter of \(400 \Omega\) resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is _________ V.

A parallel plate capacitor is having separation between plates \(0.885\) mm. It has a capacitance of \(1\,\mu\)F when the space between the plates is filled with an insulating material of resistivity \(1\times 10^{13}\,\Omega\)m and resistance \(17.7\times 10^{14}\,\Omega\). Relative permittivity of the insulating material is \(\alpha\times 10^7\). The value of \(\alpha\) is ________. (Take permittivity of free space \(=8.85\times 10^{-12}\) F/m)

A wire of length \(2\,L\) is made by joining two wires \(A\) and \(B\) of same lengths but different radii \(r\) and \(2r\) and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire \(A\) is \(p\) and that in \(B\) is \(q\) then the ratio \(p : q\) is

An electromagnetic wave travelling in the \(x-\) direction has frequency of \(2 \times 10^{14}\,Hz\) and electric field amplitude of \(27\,Vm^{-1}\) . From the options given below, which one describes the magnetic field for this wave ?

An electric field \(\overrightarrow{\mathrm{E}}=4 \mathrm{x} \hat{\mathrm{i}}-\left(\mathrm{y}^{2}+1\right) \hat{\mathrm{j}}\; \mathrm{N} / \mathrm{C}\) passes through the box shown in figure. The flux of the electric field through surfaces \(A B C D\) and \(BCGF\) are marked as \(\phi_{I}\) and \(\phi_{\mathrm{II}}\) respectively. The difference between \(\left(\phi_{\mathrm{I}}-\phi_{\mathrm{II}}\right)\) is (in \(\left.\mathrm{Nm}^{2} / \mathrm{C}\right)\)

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \(r_{d}\) and \(r_{p}\) are the radii of their circular paths respectively, then the ratio \(\frac{r_{d}}{r_{p}}\) will be \(\sqrt{ x }: 1\) where \(x\) is ..........

There are three co-centric conducting spherical shells \(A , B\) and C of radii \(a , b\) and c respectively. The potential of the spheres \(A , B\) and C respectively, are :

Match List \(- I\) (Fundamental Experiment) with List \(- II\) (its conclusion) and select the correct option from the choices given below the list \(\begin{array}{|||} \hline List\,\,-1  & List\,\,-II\,\,  \\ \hline a\,\,Franck-Hertz\,\,Experiment & i\,\,Particle\,\,nature\,\,of\,\,light \\ \hline b\,\,Photo\,\,-electric\,\,Experiment & ii\,\,Discrete\,\,energy \,\, levels\,\,of\,\,atom \\ \hline c\,\,Davison-Germer\,\,Experiment & iii\,\,Wave\,\,nature\,\,of\,\,electron \\ \hline  & iv\,\,Structure\,\,of\,\,atom  \\ \hline \end{array}\)

A rod \(C D\) of thermal resistance \(10.0\; {KW}^{-1}\) is joined at the middle of an identical rod \({AB}\) as shown in figure, The end \(A, B\) and \(D\) are maintained at \(200^{\circ} {C}, 100^{\circ} {C}\) and \(125^{\circ} {C}\) respectively. The heat current in \({CD}\) is \({P}\) watt. The value of \({P}\) is ... .