The stopping potential \(V_0\) (in \(volt\)) as a function of frequency \((v)\) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be : ................. \(eV\) (Given : Planck's constant \((h) = 6.63 \times 10^{-34}\, Js\), electron charge \(e = 1.6 \times 10^{-19}\, C\))

In a moving coil galvanometer, two moving coils \(M_1\) and \(M_2\) have the following particulars :
\(\begin{aligned}
& \mathrm{R}_1=5 \Omega, \mathrm{~N}_1=15, \mathrm{~A}_1=3.6 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_1=0.25 \mathrm{~T} \\
& \mathrm{R}_2=7 \Omega, \mathrm{~N}_2=21, \mathrm{~A}_2=1.8 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_2=0.50 \mathrm{~T}
\end{aligned}\)
Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of \(M_1\) and \(M_2\) ?

A particle of mass \(4\, {M}\) at rest disintegrates into two particles of mass \({M}\) and \(3 \,{M}\) respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass \(M\) to that of mass \(3\, {M}\) will be :

Three straight parallel current carrying conductors are shown in the figure. The force experienced by the middle conductor of length \(25\,cm\) is

A boy pushes a box of mass \(2\, kg\) with a force \(\overrightarrow{ F }=(20 \hat{ i }+10 \hat{ j }) N\) on a frictionless surface. If the box was initially at rest, then ...........  \(m\) is displacement along the \(x-\)axis after \(10\, s\).

An insulated cylinder of volume \( 60\,cm^{3} \) is filled with a gas at \( 27^{\circ}C \) and 2 atmospheric pressure. Then the gas is compressed making the final volume as \( 20\,cm^{3} \) while allowing the temperature to rise to \( 77^{\circ}C \). The final pressure is __________atmospheric pressure.

The equilateral triangle \(ABC\) is cut from a thin solid sheet of wood. (See figure) \(D, E\) and \(F\) are the mid points of its sides as shown and \(G\) is the centre of the triangle. The moment of inertia of the triangle about an axis passing through \(G\) and perpendicular to the plane of the triangle is \(I_0.\) If the smaller triangle \(DEF\) is removed from \(ABC,\) the moment of inertia of the remaining figure about the same axis is \(I.\) Then

In a series \(LCR\) circuit, the inductive reactance \(\left( X _{ L }\right)\) is \(10\, \Omega\) and the capacitive reactance \(\left( X _{ C }\right)\) is \(4\, \Omega\). The resistance \(( R )\) in the circuit is \(6\, \Omega\). The power factor of the circuit is :

A radioactive substance decays to \(\left(\frac{1}{16}\right)^{t h}\) of its initial activity in \(80\, days.\) The half life of the radioactive substance expressed in days is ... .

If e is the electronic charge, \(c\) is the speed of light in free space and \(h\) is Planck's constant, the quantity \(\frac{1}{4 \pi \varepsilon_{0}} \frac{| e |^{2}}{h c}\) has dimensions of .......

Given is a thin convex lens of glass (refractive index \(\mu\) ) and each side having radius of curvature \(R\). One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself ?

One mole of an ideal diatomic gas expands from volume V to 2 V isothermally at a temperature \(27^{\circ} C\) and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from \(27^{\circ} C\) doing the same amount of work W , then its final temperature will be (close to) ___________ \({ }^{\circ} C\).