A 2 A current carrying straight metal wire of resistance \(1 \Omega\), resistivity \(2 \times 10^{-6} \Omega m\), area of cross-section \(10 mm^2\) and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field \(\vec{B}\). The magnitude of \(B\) is _______ \(\times 10^{-1} T\) (given, \(g =10 m / s ^2\) ).

The frequency of oscillation of a mass \(m\) suspended by a spring is \(v_1\). If the length of the spring is cut to half, the same mass oscillates with frequency \(v_2\). The value of \(v_2/v_1\) is ________.

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

	List \(-I\)		List \(-II\)
\(A\).	Coefficient of Viscosity	\(I\).	\([M L^2T^{–2}]\)
\(B\).	Surface Tension	\(II\).	\([M L^2T^{–1}]\)
\(C\).	Angular momentum	\(III\).	\([M L^{-1}T^{–1}]\)
\(D\).	Rotational Kimeatic energy	\(IV\).	\([M L^0T^{–2}]\)

Two separate wires \(A\) and \(B\) are stretched by \(2 \,mm\) and \(4\, mm\) respectively, when they are subjected to a force of \(2\, N\). Assume that both the wires are made up of same material and the radius of wire \(B\) is 4 times that of the radius of wire \(A\). The length of the wires \(A\) and \(B\) are in the ratio of \(a : b\). Then \(a / b\) can be expressed as \(1 / x\) where \(x\) is

A point charge of \(10\,\mu C\) is placed at the origin. At what location on the \(X\)-axis should a point charge of \(40\,\mu\,C\) be placed so that the net electric field is zero at \(x =2\,cm\) on the \(X\)-axis ?

An air bubble of volume \(2.9 cm^3\) rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is \(17^{\circ} C\). The volume of the bubble when it reaches the surface, where the water temperature is \(27^{\circ} C\), is ___________ \(cm ^3\). ( \(g =10 m / s ^2\), density of water \(=10^3 kg / m ^3\), and 1 atm pressure is \(10^5 Pa\) )

In Young's double slits experiment, the position of \(5^{\text {th }}\) bright fringe from the central maximum is \(5\,cm\). The distance between slits and screen is \(1\,m\) and wavelength of used monochromatic light is \(600\,nm\). The separation between the slits is \(........\mu m\)

in circular plate of mass \(M\) and radius \(R\) has its density varying as \(p\left( r \right) = {p_0}\,r\) with \(P_0\) as constant and \(r\) is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is \(I = aMR^2\) . The value of the coefficient \(a\) is

If \(\epsilon_0\) denotes the permittivity of free space and \(\Phi_{\mathrm{E}}\) is the flux of the electric field through the area bounded by the closed surface, then dimension of \(\left(\epsilon_0 \frac{\mathrm{~d} \phi_{\mathrm{E}}}{\mathrm{dt}}\right)\) are that of :

The stored charge in the capacitor in steady state of the following circuit is ________ \(\mu\)C.