Two bodies of mass \(4 \mathrm{~g}\) and \(25 \mathrm{~g}\) are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

Match List \(I\) with List \(II\)

LIST\(-I\)	LIST\(-II\)
\((A)\)  Torque	\((I)\)    \(ML ^{-2} T ^{-2}\)
\((B)\)   Stress	\((II)\)   \(ML ^2 T ^{-2}\)
\((C)\)   Pressure of gradient	\((III)\)   \(ML ^{-1} T ^{-1}\)
\((D)\)   Coefficient of viscosity	\((IV)\)   \(ML ^{-1} T ^{-2}\)

Choose the correct answer from the options given below

The reading of the ammeter (A) in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is _________ A.

\({ }_{92}^{238} A \rightarrow{ }_{90}^{234} B +{ }_2^4 D + Q\) In the given nuclear reaction, the approximate amount of energy released will be \(.....\,MeV\) \(\text { [Given, mass of }{ }_{92}^{238} A =238.05079 \times 931.5\,MeV / c ^2\) \(\text { mass of }{ }_{90}^{234} B =234.04363 \times 931.5\,MeV / c ^2\) \(\text { mass of } \left.{ }_2^4 D =4.00260 \times 931.5\,MeV / c ^2\right]\)

A block of mass \(2\,kg\) moving on a horizontal surface with speed of \(4\,ms ^{-1}\) enters a rough surface ranging from \(x =0.5\,m\) to \(x =1.5\,m\). The retarding force in this range of rough surface is related to distance by \(F =- kx\) where \(k =12\,Nm ^{-1}\). The speed of the block as it just crosses the rough surface will be ........... \(\,ms ^{-1}\)

A parallel beam of monochromatic light of wavelength \(5000 \mathring A\) is incident normally on a single narrow slit of width \(0.001 \mathrm{~mm}\). The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of______________(degree).

A progressive wave travelling along the positive \(x-\) direction is represented by \(y(x, t) = A\,sin\,\left( {kx - \omega t + \phi } \right)\). Its snapshot at \(t = 0\) is given in the figure For this wave, the phase \(\phi \) is

A \(d.c.\) main supply of \(e.m.f.\, 220\, V\) is connected across a storage battery of \(e.m.f.\, 200\, V\) through a resistance of \(1\,\Omega \). The battery terminals are connected to an external resistance \('R'\) . The minimum value of \('R'\), so that a current passes through the battery to charge it is ............... \(\Omega\)

If two vectors \(\vec{A}\) and \(\vec{B}\) having equal magnitude \(\mathrm{R}\) are inclined at an angle \(\theta\), then...

Proton \((P)\) and electron \((e)\) will have same deBroglie wavelength when the ratio of their momentum is (assume, \(m _{ p }=1849\,m _{ e }\))

Abeam of unpolarised light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^{\circ}\) relative to that of \(A\). The intensity of emergent light is :

A guitar string of length \(90\,cm\) vibrates with a fundamental frequency of \(120\,Hz.\) The length of the string producing a fundamental frequency of \(180\,Hz\) will be \(...........cm\).

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is \(30 \;\mathrm{cm}\) and the refractive index of the lens material is \(1.5 .\) then the focal length of the lens (in \(\mathrm{cm}\) ) is