Two point dipoles of dipole moment \({\vec P_1}\) and \({\vec P_2}\) are at a distance \(x\) from each other and  \({\vec P_1}\) || \({\vec P_2}\). The force between the dipoles is

In two separate Young's double-slit experimental set-ups, two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slit separations and that of the wavelengths of light used are \(2: 1\) and \(1: 2\) respectively. The corresponding ratio of the distances between the slits and the respective screens ( \(D_1 / D_2\) ) is ___________ .

A straight wire carrying a current of \(14\,A\) is bent into a semicircular are of radius \(2.2\,cm\) as shown in the figure. The magnetic field produced by the current at the centre \((O)\) of the arc. is \(.........\,\times 10^{-4}\, T\)

Following statements are given : \((1)\) The average kinetic energy of a gas molecule decreases when the temperature is reduced. \((2)\) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. \((3)\) The average kinetic energy of a gas molecule decreases with increases in volume. \((4)\) Pressure of a gas increases with increase in temperature at constant pressure. \((5)\) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below:

In an experiment to determine the period of a simple pendulum of length \(1\, m\), it is attached to different spherical bobs of radii \(r_1\) and \(r_2\) . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be \(5\times10^{-4}\, s\), the difference in radii, \(\left| {{r_1} - {r_2}} \right|\) is best given by .... \(cm\)

In a spring gun having spring constant \(100\, {N} / {m}\) a small ball \('B'\) of mass \(100\, {g}\) is put in its barrel (as shown in figure) by compressing the spring through \(0.05\, {m}\). There should be a box placed at a distance \('d'\) on the ground so that the ball falls in it. If the ball leaves the gun horizontally at a height of \(2\, {m}\) above the ground. The value of \(d\) is \(....{m} .\) \(\left(g=10\, {m} / {s}^{2}\right)\)

Young’s moduli of two wires \(A\) and \(B\) are in the ratio \(7 : 4\). Wire \(A\) is \(2\, m\) long and has radius \(R\). Wire \(A\) is \(2\, m\) long and has radius \(R\). Wire \(B\) is \(1.5\, m\) long and has radius \(2\, mm\). If the two wires stretch by the same length for a given load, then the value of \(R\) is close to ......... \(mm\)

The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is \(x: 4\) where \(x\) is ..... .

Two radioactive materials \(A\) and \(B\) have decay constants \(10\,\lambda \) and \(\lambda \), respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of \(B\) will be \(1/e\) after a time

A power transmission line feeds input power at \(2300\,V\) to a step down transfonner with its primary windings having  \(4000\) turns, giving the output power at \(230\,V.\)  If the current in the primary of the transformer is  \(5\,A,\) and its efficiency is \(90\%,\)  the output current would be......\(A\)

A body is projected at \(t = 0\) with a velocity \(10\,ms^{-1}\) at an angle of \(60^o\) with the horizontal. The radius of curvature of its trajectory at \(t=1\,s\) is \(R.\) Neglecting air resistance and taking acceleration due to gravity \(g = 10\,ms^{-2},\) the radius of \(R\) is   ........ \(m\)

The frequency of revolution of the electron in Bohr's orbit varies with \(n\), the principal quantum number as _______.

Given below are two statements:
Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement II: For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon.
In the light of the above statements, choose the correct answer from the options given below: