Two identical conducting spheres with negligible volume have \(2.1\, nC\) and \(-0.1\, nC\) charges, respectively. They are brought into contact and then separated by a distance of \(0.5 \,m\). The electrostatic force acting between the spheres is \(.......... \, \times 10^{-9} \,N\) [Given : \(4 \pi \varepsilon_{0}=\frac{1}{9 \times 10^{9}} SI\) unit]

An object is taken to a height above the surface of earth at a distance \(\frac{5}{4} R\) from the centre of the earth. Where radius of earth, \(R=6400\,km\). The percentage decrease in the weight of the object will be \(....\%\)

In a physical balance working on the principle of moments, when \(5\, mg\) weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

For the series LCR circuit connected with 220 V , 50 Hz a.c source as shown in the figure, the power factor is \(\frac{\alpha}{10}\). The value of \(\alpha\) is _________

A sonometer wire of length \(114\, cm\) is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio \(1 : 3 : 4\) ?

The electric current in a circular coil of four turns produces a magnetic induction \(32\,T\) at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be \(..........\,T\)

Starting from the origin at time \(t=0,\) with initial velocity \(5 \hat{ j }\, ms ^{-1},\) a particle moves in the \(x-y\) plane with a constant acceleration of \((10 \hat{ i }+4 \hat{ j })\, ms ^{-2}\). At time \(t\), its coordinates are \(\left(20\, m , y _{0}\, m \right) .\) The values of \(t\) and \(y _{0},\) are respectively

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k=3 and permeability \(\mu=2\mu_{0}\), is
( \(\mu_0=\) permeability of vacuum)

A parallel plate capacitor is made of two plates of length \(l\), width \(w\) and separated by distance \(d\). A dielectric slab ( dielectric constant \(K\)) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force \(F = -\frac{{\partial U}}{{\partial x}}\) where \(U\) is the energy of the capacitor when dielectric is inside the capacitor up to distance \(x\) (See figure). If the charge on the capacitor is \(Q\) then the force on the dielectric when it is near the edge is

Two different wires having lengths \(L _{1}\) and \(L _{2}\) and respective temperature coefficient of linear expansion \(\alpha_{1}\) and \(\alpha_{2},\) are joined end-to-end. Then the effective temperature coefficient of linear expansion is

The electric field of a plane electromagnetic wave propagating along the \(x\) direction in vacuum is \(\overrightarrow{ E }= E _{0} \hat{ j } \cos (\omega t - kx )\). The magnetic field \(\overrightarrow{ B },\) at the moment \(t =0\) is :