Consider a circular coil of wire carrying constant current \(I\), forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by \(\phi_{i} .\) The magnetic flux through the area of the circular coil area is given by \(\phi_{0} .\) Which of the following option is correct?

Match List - I with List - II.

List - I	List - II
(A) Permeability of free space	(I) \(\left[\mathrm{M} \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\)
(B) Magnetic field	(II) \(\left[\mathrm{M} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\)
(C) Magnetic moment	(III) \(\left[\mathrm{M} \mathrm{~L} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]\)
(D) Torsional constant	(IV) \(\left[\mathrm{L}^2 \mathrm{~A}\right]\)

Choose\(\text{ }\)the\(\text{ }\)correct\(\text{ }\)answer\(\text{ }\)from\(\text{ }\)the\(\text{ }\)options\(\text{ }\)given\(\text{ }\)below\(\text{ }\):

The specific heat of water \(=4200\, J\, kg ^{-1}\, K ^{-1}\) and the latent heat of ice \(=3.4 \times 10^{5}\, J\, kg ^{-1}.\) \(100\) grams of ice at \(0^{\circ} C\) is placed in \(200\, g\) of water at \(25^{\circ} C\). The amount of ice that will melt as the temperature of water reaches \(0^{\circ} C\) is close to (in \(grams\)) 

A radioactive nucleus \(A\) with a half life \(T\), decays into a nucleus \(B.\) At \(t = 0\), there is no nucleus \(B\). At sometime \(t\), the ratio of the number of \(B\) to that of \(A\) is \(0.3\). Then, \(t\) is given by

A rod \(C D\) of thermal resistance \(10.0\; {KW}^{-1}\) is joined at the middle of an identical rod \({AB}\) as shown in figure, The end \(A, B\) and \(D\) are maintained at \(200^{\circ} {C}, 100^{\circ} {C}\) and \(125^{\circ} {C}\) respectively. The heat current in \({CD}\) is \({P}\) watt. The value of \({P}\) is ... .

Electric field in a plane electromagnetic wave is given by \({E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}\) The velocity of electromagnetic wave in this medium is : (Given \({C}=\) speed of light in vacuum)

Equation of travelling wave on a stretched string of linear density \(5\,g/m\) is \(y = 0.03\,sin\,(450\,t -9x)\) where distance and time are measured in \(SI\) united. The tension in the string is ... \(N\)

In the experiment for measurement of viscosity ' \(\eta\) ' of given liquid with a ball having radius \(R\), consider following statements.
A. Graph between terminal velocity V and R will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \(\eta\) will change.
Choose the correct answer from the options given below: