Two concentric circular coils with radii \(1\,cm\) and \(1000\,cm\), and number of turns \(10\) and \(200\) respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be \(.........\times 10^{-8}\,H\)(Take, \(\pi^2=10\))

Match List \(I\) with List \(II\)

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

Choose the correct answer from the options given below :

A body of mass \(8\,kg\) and another of mass \(2\, kg\) are moving with equal kinetic energy. The ratio of their respective momenta will be.

A heavy iron bar, of weight \(\mathrm{W}\) is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle \(\theta\) with the horizontal. The weight experienced by the person is _______.

A circular coil having \(200\) turns, \(2.5 \times 10^{-4} \mathrm{~m}^2\) area and carrying \(100 \mu \mathrm{A}\) current is placed in a uniform magnetic field of \(1 \mathrm{~T}\). Initially the magnetic dipole moment \((\vec{M})\) was directed along \(\vec{B}\). Amount of work, required to rotate the coil through \(90^{\circ}\) from its initial orientation such that \(\overrightarrow{\mathrm{M}}\) becomes perpendicular to \(\vec{B}\) is _______ \(\mu \mathrm{J}\).

In an electrical circuit, a battery is connected to pass \(20\, C\) of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at \(15\, V\). The work done by the battery is ........... \(J\).

A particle of mass \(m\) is acted upon by a force \(F\) given by the empirical law \(F = \frac{R}{{{t^2}}}\,v(t)\). If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot 

The volume contraction of a solid copper cube of edge length 10 cm , when subjected to a hydraulic pressure of \(7 \times 10^6 \mathrm{~Pa}\), would be ____ \(\mathrm{mm}^3\).
(Given bulk modulus of copper \(=1.4 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\) )

A metal wire of uniform mass density having length \(L\) and mass \(M\) is bent to form a semicircular arc and a particle of mass \(m\) is placed at the centre of the arc. The gravitational force on the particle by the wire is _______.

A block of \(\sqrt{3}\,kg\) is attached to a string whose other end is attached to the wall. An unknown force \(F\) is applied so that the string makes an angle of \(30^{\circ}\) with the wall. The tension \(T\) is \(...........\,N\) :(Given \(g =10\,ms ^{-2}\) )

A bar magnet having a magnetic moment of \(2.0 \times\) \(10^{5} \; JT ^{-1}\), is placed along the direction of uniform magnetic field of magnitude \(B =14 \times 10^{-5}\; T\). The work done in rotating the magnet slowly through \(60^{\circ}\) from the direction of field is .............. \(J\) 

A circular coil of radius \(10\, cm\) is placed in a uniform magnetic field of \(3.0 \times 10^{-5}\, T\) with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in \(0.2\,s.\) The maximum value of \(EMF\) induced (in \(\mu V\) ) in the coil will be close to the integer\(....\mu V\)