The magnetic susceptibility of a material of a rod is \(499 .\) Permeability in vaccum is \(4 \pi \times 10^{-7}\; {H} / {m}\). Absolute permeability of the material of the rod is \(....\,\pi \times 10^{-4} {H} / {m}\)

A spherically symmetric charge distribution is characterised by a charge density having the following variations \(\rho (r)\, = \,{\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(r < R\) \(\rho (r)\,=\,0\) for \(r\, \ge \,R\) Where \(r\) is the distance from the centre of the charge distribution \(\rho _0\) is a constant. The electric field at an internal point \((r < R)\) is

Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength \(\lambda\). The value of principal quantum number ' \(n\) ' of the excited state will be: (\(R\): Rydberg constant)

A solid sphere, of radius \(R\) acquires a terminal velocity \(\nu_1 \) when falling (due to gravity) through a viscous fluid having a coefficient of viscosity \(\eta \). The sphere is broken into \(27\) identical solid spheres. If each of these spheres acquires a terminal velocity, \(\nu_2\), when falling through the same fluid, the ratio \((\nu_1/\nu_2)\) equals

In free space, an electromagnetic wave of \(3 \; GHz\) of \(3 \; GHz\) frequency strikes over the edge of an object of size \(\frac{\lambda}{100}\), where \(\lambda\) is the wavelength of the wave in free space. The phenomenon, which happens there will be .....

Four particles \(A, B, C\) and \(D\) with masses \(m_A=m, m_B=2m, m_C=3m\) and \(m_D=4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

Three point particles of masses \(1.0\; \mathrm{kg} .1 .5 \;\mathrm{kg}\) and \(2.5\; kg\) are placed at three comers of a right angle triangle of sides \(4.0\; \mathrm{cm}, 3.0 \;\mathrm{cm}\) and \(5.0\; \mathrm{cm}\) as shown in the figure. The center of mass of the system is at a point

If \(K_{1}\) and \(K_{2}\) are the thermal conductivities \(L_{1}\) and \(L _{2}\) are the lengths and \(A _{1}\) and \(A _{2}\) are the cross sectional areas of steel and copper rods respectively such that \(\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2\). Then, for the arrangement as shown in the figure. The value of temperature \(T\) of the steel - copper junction in the steady state will be ........... \(^{\circ} C\)

A Carnot freezer takes heat from water at \(0\,^oC\) inside it and rejects it to the room at a temperature of \(27\,^oC\). The latent heat of ice is \(336 \times 10^3\, J\,kg^{-1}\).  lf \(5\, kg\) of water at \(0\,^oC\) is converted into ice at  \(0\,^oC\) by the freezer, then the energy consumed by the freezer is close to

Consider \(\mathrm{I}_1\) and \(\mathrm{I}_2\) are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If \(\mathrm{L}_1=\) self inductance of coil \(1, \mathrm{M}_{12}=\) mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be ________.

An electromagnetic wave of frequency \(5\, GHz ,\) is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are \(2 .\) Its velocity in this medium is \(\times 10^{7}\, m / s\)