A student measures the time period of \(100\) oscillations of a simple pendulum four times. The data set is  \(90\;s\) ,\(91\;s \), \(95\;s\) and \(92\;s\). If the minimum division in the  measuring clock is \(1\;s\), then the reported mean time should be

For the network shown below, the value \(V _{ B }- V _{ A }\) is_______ \(V\)

A series \(L C R\) circuit has \(L=0.01\,H, R=10\,\Omega\) and \(C =1\,\mu F\) and it is connected to ac voltage of amplitude \(\left( V _{ m }\right) 50\,V\). At frequency \(60 \%\) lower than resonant frequency, the amplitude of current will be approximately \(...............\,mA\)

Two identical conducting spheres \(A\)  and \(B,\)  carry equal charge. They are separated by a distance much larger than their diameter, and the force between them is \(F\) . A third identical conducting sphere, \(C,\)  is uncharged. Sphere \(C\)  is first touched to \(A,\) then to \(B,\)  and then removed. As a result, the force between \(A\)  and \(B\)  would be equal to

A square loop of side \(20\, {cm}\) and resistance \(1\, \Omega\) is moved towards right with a constant speed \({v}_{0}\). The right arm of the loop is in a uniform magnetic field of \(5\, {T}\). The field is perpendicular to the plane of the loop and is going into it. The loop is connected to a network of resistors each of value \(4\, \Omega\). What should be the value of \(v_{0}\) so that a steady current of \(2\, {mA}\) flows in the loop ?

A particle of mass \(m\) and charge \(q\) is in an electric and magnetic field given by \(\vec E = 2\hat i + 3\hat j ;\, B = 4\hat j + 6\hat k\) The charged particle is shifted from the origin to the point \(P(x = 1 ;\, y = 1)\) along a straight path. The magnitude of the total work done is

10 mole of oxygen is heated at constant volume from \(30^{\circ} C\) to \(40^{\circ} C\). The change in the internal energy of the gas is _________ cal. (The molecular specific heat of oxygen at constant pressure, \(C _{ p }=7 cal . / mol ^{\circ} C\) and \(\left.R =2 cal . / mol ^{\circ} C .\right)\)

The distance of centre of mass from end \(A\) of a one dimensional rod \(( AB )\) having mass density \(\rho=\rho_{0}\left(1-\frac{ x ^{2}}{ L ^{2}}\right)\,kg / m\) and length \(L\) (in meter) is \(\frac{3 L }{\alpha} m\). The value of \(\alpha\) is \(\ldots \ldots \ldots . .\) (where \(x\) is the distance form end \(A\) )

A moving coil of galvanometer when shunted with \(2\,\Omega\) resistance gives a full scale deflection for a current of \(500\) mA. When a resistance of \(470\,\Omega\) is connected in series it gives a full scale deflection for \(10\) V potential applied on it. The value of resistance of galvanometer coil is __________ \(\Omega\).

A thin infinite sheet charge and an infinite line charge of respective charge densities \(+\sigma\) and \(+\lambda\) are placed parallel at \(5\,m\) distance from each other. Points \(P\) and \(Q\), are at \(\frac{3}{\pi} m\) and \(\frac{4}{\pi} m\) perpendicular distance from line charge towards sheet charge, respectively. \(E_P\) and \(E_Q\) are the magnitudes of resultant electric field intensities at point \(P\) and \(Q\), respectively. If \(\frac{E_p}{E_Q}=\frac{4}{a}\) for \(2|\sigma|=|\lambda|\). Then the value of \(a\) is ...........