The electrostatic potential due to an electric dipole at a distance '\(r\)' varies as _______.

Young's modulus is determined by the equation given by \(\mathrm{Y}=49000 \frac{\mathrm{m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}\) where \(\mathrm{M}\) is the mass and \(\ell\) is the extension of wre used in the experiment. Now error in Young modules \((\mathrm{Y})\) is estimated by taking data from \(M-\ell\) plot in graph paper. The smallest scale divisions are \(5 \mathrm{~g}\) and \(0.02\) \(\mathrm{cm}\) along load axis and extension axis respectively. If the value of \(M\) and \(\ell\) are \(500 \mathrm{~g}\) and \(2 \mathrm{~cm}\) respectively then percentage error of \(\mathrm{Y}\) is _______.

A metallic surface is illuminated with radiation of wavelength \(\lambda\), the stopping potential is \(V_0\). If the same surface is illuminated with radiation of wavelength \(2 \lambda\), the stopping potential becomes \(\frac{V_0}{4}\). The threshold wavelength for this metallic surface will be -

A Carnot's engine works as a refrigerator between \(250\, K\) and \(300\, K\). It receives \(500\, cal\) heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is ..... \(J\)

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at \(P\), in the region, is found to vary between in the limits \(589.0\,V\) to \(589.8\, V\). What is the potential at a point on the sphere whose radius vector makes an angle of \(60^o\) with the direction of the field ?........\(V\)

In the experiment of calibration of voltmeter, a standard cell of \(e.m.f\,\,1.1\,volt\) is balanced against \(440\,cm\) of potential wire. The potential difference across the ends of resistance is found to balance against \(220\,cm\) of the wire. The corresponding reading of voltmeter is \(0.5\,volt.\) The error in the reading of volmeter will be .................. \(volt\)

If \(L , C\) and \(R\) are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

\(\lim _{n \rightarrow \infty}\left[\frac{1}{n}+\frac{n}{(n+1)^{2}}+\frac{n}{(n+2)^{2}}+\ldots \ldots .+\frac{n}{(2 n-1)^{2}}\right]\) is equal to ...... .

A source of sound \(A\) emitting waves of frequency \(1800\,Hz\) is falling towards ground with a terminal speed \(v.\) The observer \(B\) on the ground directly beneath the source receives waves of frequency \(2150\,Hz.\) The source \(A\) receives waves, reflected from ground of frequency nearly ..... \(Hz\) (Speed of sound \(= 343\,m/s\) )

Consider the line \(L\) given by the equation \(\frac{x-3}{2}=\frac{y-1}{1}=\frac{z-2}{1}\). Let \(Q\) be the mirror image of the point \((2,3,-1)\) with respect to \(L\). Let a plane \(P\) be such that it passes through \(Q\), and the line \(L\) is perpendicular to \(P.\) Then which of the following points is on the plane \(P\) ?

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is

If \(I=\int\limits_{1}^{2} \frac{d x}{\sqrt{2 x^{3}-9 x^{2}+12 x+4}},\) then

A series \(LCR\) circuit of \(R=5\, \Omega, L=20\, {mH}\) and \({C}=0.5 \,\mu \,{F}\) is connected across an \({AC}\) supply of \(250\, V\), having variable frequency. The power dissipated at resonance condition is \(.....\,\times 10^{2}\, {W}\)