Two coils \(P\) and \(Q\) are separated by some distance. When a current of \(3\, A\) flows through coil \(P\) a magnetic flux of \(10^{-3}\, Wb\) passes through \(Q\). No current is passed through \(Q\). When no current passes through \(P\) and a current of \(2\, A\) passes through \(Q\), the flux through \(P\) is

A hanging mass \(M\) is connected to a four times bigger mass by using a string-pulley arrangement. as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by \(2\,Mg\) force. In this situation. tension in the string is \(\frac{x}{5}\) \(Mg\) for \(x =\) Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given \(g=\) acceleration due to gravity)

A long straight wire with a circular crosssection having radius \(R\), is carrying a steady current \(I\). The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance \(r\;( r < R )\) from its centre will be

Consider a rectangular sheet of solid material of length \(\ell=9 \mathrm{~cm}\) and width \(\mathrm{d}=4 \mathrm{~cm}\). The coefficient of linear expansion is \(\alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1}\) at room temperature and one atmospheric pressure. The mass of sheet \(\mathrm{m}=0.1 \mathrm{~kg}\) and the specific heat capacity \(\mathrm{C}_{\mathrm{v}}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\). If the amount of heat supplied to the material is \(8.1 \times 10^2 \mathrm{~J}\) then change in area of the rectangular sheet is :-

A square loop \(\mathrm{PQRS}\) having \(10\) turns, area \(3.6 \times\) \(10^{-3} \mathrm{~m}^2\) and resistance \(100 \Omega\) is slowly and uniformly being pulled out of a uniform magnetic field of magnitude \(\mathrm{B}=0.5 \mathrm{~T}\) as shown. Work done in pulling the loop out of the field in \(1.0 \mathrm{~s}\) is _______ \(\times 10^{-6} \mathrm{~J}\).

A particle of charge \(1.6 \mu \mathrm{C}\) and mass \(16 \mu \mathrm{~g}\) is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is ________ S. \((\pi=3.14)\)

A man grows into a giant such that his linear dimensions increase by a factor of \(9\). Assuming that his density remains same, the stress in the leg will change by a factor of

A ray of light of intensity \(I\) is incident on a parallel glass slab at point \(A\) as shown in diagram. It undergoes partial reflection and refraction. At each reflection, \(25\%\) of incident energy is reflected. The rays \(AB\) and \(A'B'\) undergo interference. The ratio of \(I_{max}\) and \(I_{min}\) is

An expression of energy density is given by \(u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)\), where \(\alpha, \beta\) are constants, \(x\) is displacement, \(k\) is Boltzmann constant and \(t\) is the temperature. The dimensions of \(\beta\) will be.

The give graph shown variation (with distance \(r\) from centre) of

A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \(\omega_0\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?