If \(‘M’\) is the mass of water that rises in a capillary tube of radius \(‘r’,\) then mass of water which will rise in a capillary tube of radius \(‘2r’\) is

The moment of inertia of a circular ring of mass \(M\) and diameter r about a tangential axis lying in the plane of the ring is :

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

List \(I\) (Physical Quantity)	List \(II\) (Dimensional Formula)
\((A)\) Pressure gradient	\((I)\) \(\left[ M ^0 L ^2 T ^{-2}\right]\)
\((B)\) Energy density	\((II)\) \(\left[ M ^1 L ^{-1} T ^{-2}\right]\)
\((C)\) Electric Field	\((III)\) \(\left[ M ^1 L ^{-2} T ^{-2}\right]\)
\((D)\) Latent heat	\((IV)\) \(\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]\)

Choose the correct answer from the options given below:

An upright object is placed at a distance of \(40\, cm\) in front of a convergent lens of focal length \(20\, cm\). A convergent mirror of focal length \(10\, cm\) is placed at a distance of \(60\, cm\) on the other side of the lens. The position and size of the final image will be

A block moving horizontally on a smooth surface with a speed of \(40\, {ms}^{-1}\) splits into two equal parts. If one of the parts moves at \(60\, {ms}^{-1}\) in the same direction, then the fractional change in the kinetic energy will be \(x: 4\) where \(x=..... .\)

The electric fields of two plane electromagnetic plane waves in vacuum are given by \(\overrightarrow{\mathrm{E}}_{1}=\mathrm{E}_{0} \hat{\mathrm{j}} \cos (\omega \mathrm{t}-\mathrm{kx})\) and \(\overrightarrow{\mathrm{E}}_{2}=\mathrm{E}_{0} \hat{\mathrm{k}} \cos (\omega \mathrm{t}-\mathrm{ky})\) At \(t=0,\) a particle of charge \(q\) is at origin with a velocity \(\overrightarrow{\mathrm{v}}=0.8 \mathrm{c} \hat{\mathrm{j}}\) (\(c\) is the speed of light in vacuum). The instantaneous force experienced by the particle is 

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is _______.

Arrange the following electromagnetic radiations per quantum in the order of increasing energy :- \(A\) : Blue light \(B\) : Yellow light \(C\) : X-ray \(D\) : Radiowave

Consider a spherical shell of radius \(R\) at temperature \(T\). The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume\(E=\) \(\frac{U}{V} \propto {T^4}\) and pressure \(P = \frac{1}{3}\left( {\frac{U}{V}} \right)\) If the shell now undergoes an adiabatic expansion the relation between \(T\) and \(R\) is

A proton and an \(\alpha\) -particle, having kinetic energies \(K _{ p }\) and \(K _{\alpha},\) respectively, enter into \(a\) magnetic field at right angles. The ratio of the radii of trajectory of proton to that of \(\alpha\) -particle is \(2: 1 .\) The ratio of \(K _{ p }: K _{\alpha}\) is :

In Young's double slits experiment, the position of \(5^{\text {th }}\) bright fringe from the central maximum is \(5\,cm\). The distance between slits and screen is \(1\,m\) and wavelength of used monochromatic light is \(600\,nm\). The separation between the slits is \(........\mu m\)

For a series \(LCR\) circuit, \(I\) vs \(\omega\) curve is shown \((A)\) To the left of \(\omega_{r}\), the circuit is mainly capacitive. \((B)\) To the left of \(\omega_{r}\), the circuit is mainly inductive. \((C)\) At \(\omega_{r}\), impedance of the circuit is equal to the resistance of the circuit. \((D)\) At \(\omega_{t}\), impedance of the circuit is \(0\). Choose the most appropriate answer from the options given below