A time dependent force \(F = 6t\) acts on a particle of mass \(1\ kg\). If the particle starts from rest, the work done by the force during the first \(1\) secand will be ............... \(\mathrm{J}\)

In a compound microscope, the magnified virtual image is formed at a distance of \(25\, cm\) from the eye-piece. The focal length of its objective lens is \(1\, cm .\) If the magnification is \(100\) and the tube length of the microscope is \(20\, cm ,\) then the focal length of the eye-piece lens (in \(cm\) ) is

For the given circuit the current through battery of \(6\,V\) just after closing the switch ' \(S\) ' will be\(.......A\).

Match List\(-I\) with List\(-II:\)

List\(-I\)	List\(-II\)
\((A)\) \(3\) Translational degrees of freedom	\((I)\) Monoatomic gases
\((B)\) \(3\) Translational,\(2\) rotational degrees of freedoms	\((II)\) Polyatomic gases
\((C)\) \(3\) Translational,\(2\) rotational and \(1\) vibrational degrees of freedom	\((III)\) Rigid diatomic gases
\((D)\) \(3\) Translational,\(3\) rotational and more than one vibrational degrees of freedom	\((IV)\) Nonrigid diatomic gases

Choose the correct answer from the options given below:

If velocity \([V],\) time \([T]\) and force \([F]\) are chosen as the base quantities, the dimensions of the mass will be

Two stars of masses \(m\) and \(2\, m\) at a distance \(d\) rotate about their common centre of mass in free space. The period of revolution is

\(5\) moles of unknown gas is heated at constant volume from \(10 \, °C\) to \(20 \, °C\). The molar specific heat of this gas at constant pressure \(c_p = 8\) cal/mol.°C and \(R = 8.36\) J/mol.°C. The change in the internal energy of the gas is _______ calorie.

In a photoelectric experiment, increasing the intensity of incident light :

Two streams of photons, possessing energies to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be.

In a Young's double slit experiment, slits are separated by \(0.5\ mm\), and the screen is placed \(150\ cm\) away. A beam of light consisting of two wavelengths, \(650\ nm\) and \(520\ nm\), is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is...... \(mm\)

A alternating current at any instant is given by \(i=\left[6+\sqrt{56} \sin \left(100 \pi t+\frac{\pi}{3}\right)\right] A\). The rms value of the current is _________ A.

A steam engine intakes \(50\, g\) of steam at \(100^{\circ} C\) per minute and cools it down to \(20^{\circ} C\). If latent heat of vaporization of steam is \(540 \,cal g ^{-1}\), then the heat rejected by the steam engine per minute is .........\(\times 10^{3}\)\(cal.\)

Two harmonic waves moving in the same direction superimpose to form a wave \(\mathrm{x}=\mathrm{a} \cos (1.5 \mathrm{t}) \cos (50.5 \mathrm{t})\) where \(t\) is in seconds. Find the period with which they beat (close to nearest integer)