A current of \(6\, A\) enters one corner \(P\) of an equilateral triangle \(PQR\) having \(3\) wires of resistance \(2 \,\Omega\) each and leaves by the corner \(R\). The currents \(i_{1}\) in ampere is ........ .

A beaker contains a fluid of density \(\rho \, kg / m^3\), specific heat \(S\, J / kg\,^oC\) and viscosity \(\eta \). The beaker is filled upto height \(h\). To estimate the rate of heat transfer per unit area \((Q / A)\) by convection when beaker is put on a hot plate, a student proposes that it should depend on \(\eta \,,\,\left( {\frac{{S\Delta \theta }}{h}} \right)\) and \(\left( {\frac{1}{{\rho g}}} \right)\) when \(\Delta \theta \) (in \(^oC\)) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for \((Q / A)\) is

A particle of mass \(M\) is moving in a circle of fixed radius \(R\) in such a way that its centripetal acceleration at time \(t\) is given by \(n^2Rt^2\) where \(n\) is a constant. The Power delivered to the particle by the force acting on it, is

A smooth wire of length \(2\pi r\) is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed \(\omega\) about the vertical diameter \(AB\), as shown in figure, the bead is at rest with respect to the circular ring at position \(P\) as shown. Then the value of \(\omega^2\) is equal to

In an \(A.C.\) circuit, the instantaneous \(e.m.f\) and current are given by. \(e=100\) \(sin\) \(20t\) \(i=20sin\) \(\left( {30t - \frac{\pi }{4}} \right)\) In one cycle of \(A.C.\), the average power consumed by the circuit and the wattless current are, respectively

A photon of wavelength \(\lambda \) is scattered from an electron, which was at rest. The wavelength shift \(\Delta \lambda \) is three times of \( \lambda \) and the angle of scattering \(\theta \) is \(60^o\) . The angle at which the electron recoiled is \(\phi \). The value of \(tan\,\phi \) is : ( electron speed is much smaller than the speed of light)

A square loop of edge length \(2 \mathrm{~m}\) carrying current of \(2 \mathrm{~A}\) is placed with its edges parallel to the \(\mathrm{x}-\mathrm{y}\) axis. A magnetic field is passing through the \(x-y\) plane and expressed as \(\vec{B}=B_0(1+4 x) \hat{k}\), where \(\mathrm{B}_0=5 \mathrm{~T}\). The net magnetic force experienced by the loop is _______ \(\mathrm{N}\).

Eight equal drops of water are falling through air with a steady speed of \(10\,cm / s\). If the drops coalesce, the new velocity is \(.........\,cm/s\)

\(K_1\) and \(K_2\) be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength \(\lambda_1\) and \(\lambda_2\), respectively. If \(\lambda_1=2\lambda_2\) then the work function of material is given by:

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is _______.

A mass \(M\) hangs on a massless rod of length \(l\) which rotates at a constant angular frequency. The mass \(M\) moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity \(\omega .\) The angular momentum of \(M\) about point \(A\) is \(L _{ A }\) which lies in the positive \(z\) direction and the angular momentum of \(M\) about \(B\) is \(L _{ B }\). The correct statement for this system is

A metallic sphere cools from \(50^{\circ} C\) to \(40^{\circ} C\) in \(300 \,s.\) If atmospheric temperature around is \(20^{\circ} C ,\) then the sphere's temperature after the next \(5\) minutes will be close to\(.....C\)