The dipole moment of a circular loop carrying a current \(I\), is \(m\) and the magnetic field at the centre of the loop is \(B_1\) . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is \(B_2\) . The ratio \(\frac{{{B_1}}}{{{B_2}}}\) is

A box weighs \(196 \;\mathrm{N}\) on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to ....... \(N\) (Take \(\mathrm{g}=10\; \mathrm{ms}^{-2}\) at the north pole and the radius of the earth \(=6400\; \mathrm{km}\))

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes \(0.01 \,cm ^{3}\) of oleic acid per \(cm ^{3}\) of the solution. Then you make a thin film of this solution (monomolecular thickness) of area \(4\, cm ^{2}\) by considering \(100\) spherical drops of radius \(\left(\frac{3}{40 \pi}\right)^{\frac{1}{3}} \times 10^{-3}\, cm .\) Then the thickness of oleic acid layer will be \(x \times 10^{-14} \,m\). Where \(x\) is ...... .

If the screw on a screw-gauge is given six rotations, it moves by \(3\; \mathrm{mm}\) on the main scale. If there are \(50\) divisions on the circular scale the least count of the screw gauge is

The distance between two consecutive points with phase difference of \(60^{\circ}\) in a wave of frequency \(500\,Hz\) is \(6.0\,m\). The velocity with which wave is traveling is \(.........km / s\)

Muon \((\mu ^{-1})\) is negatively charged \(\left( {\left| q \right| = \left| e \right|} \right)\) with a mass \(m_{\mu}\, = 200\,m_e\), where \(m_e\) is the mass of the electron and \(e\) is the electronic charge. If \(\mu ^{-1}\) is bound to a proton to form a hydrogen like atom, identify the correct statements \((A)\) Radius of the muonic orbit is \(200\) times smaller than that of the electron \((B)\) the speed of the \(\mu ^{-1}\) in the \(n^{th}\) orbit is \(\frac{1}{{200}}\) times that of the election in the \(n^{th}\) orbit \((C)\) The Ionization energy of muonic atom is \(200\) times more than that of an hydrogen atom \((D)\) The momentum of the muon in the \(n^{th}\) orbit is \(200\) times more than that of the electron

An electron of a hydrogen like atom, having \(Z=4\), jumps from \(4^{\text {th }}\) energy state to \(2^{\text {nd }}\) energy state, The energy released in this process, will be \(.........eV\) \((\) Given \(Rch =13.6\,eV )\) Where \(R =\) Rydberg constant \(c=\) Speed of light in vacuum \(h =\) Planck's constant

A galvanometer is used in laboratory for the null point in electrical experiments. If, on passing a current of \(6 \,m A\) it produces a deflection of \(2^{\circ},\) its figure of merit is close to :

The equation of a circle is given by \(x^2+y^2=a^2\), where \(a\) is the radius. If the equation is modified to change the origin other than \((0,0)\), then find out the correct dimensions of \(A\) and \(B\) in a new equation: \((x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2\).The dimensions of \(t\) is given as \(\left[ T ^{-1}\right]\).

Given below are two statements: One is labelled as Assertion \((A)\) and the other is labelled as Reason \((R).\) Assertion \((A)\) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle. Reason \((R)\) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.