A sand dropper drops sand of mass \(m(t)\) on a conveyer belt at a rate proportional to the square root of speed \((v)\) of the belt, i.e. \(\frac{\mathrm{dm}}{\mathrm{dt}} \propto \sqrt{v}\). If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

In this figure the resistance of the coil of galvanometer \(G\) is \(2\,\Omega\). The emf of the cell is \(4\,V\). The ratio of potential difference across \(C_1\) and \(C_2\) is:

\(5\,g\) and radius \(1\,cm\) is fixed to a thin stick \(AB\) of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about \(AB\) at \(25\) rotations per second in \(5\,s\) is close to

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into \(a\) square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:

An elevator in a building can carry a maximum of \(10\) persons, with the average mass of each person being \(68\; kg\). The mass of the elevator itself is \(920\; kg\) and it moves with a constant speed \(3\; \mathrm{m} / \mathrm{s}\). The frictional force opposing the motion is \(6000 \;\mathrm{N}\). If the elevator is moving up with its full capacity, the 10.Power delivered by the motor to the elevator \(\left(\mathrm{g}=10 \;\mathrm{m} / \mathrm{s}^{2}\right)\) must be at least .............. \(\mathrm{W}\)

Speed of an electron in Bohr's \(7^{\text {th }}\) orbit for Hydrogen atom is \(3.6 \times 10^6\,m / s\). The corresponding speed of the electron in \(3^{\text {rd }}\) orbit, in \(m / s\) is \(........\times 10^6\)

When a particle of mass \(m\) is attached to a vertical spring of spring constant \(k\) and released, its motion is described by \(y ( t )= y _{0} \sin ^{2} \omega t ,\) where \('y'\) is measured from the lower end of unstretched spring. Then \(\omega\) is

The current flowing through \(R _2\) is:

If two metallic plates of equal thicknesses and thermal conductivities \({K_1}\) and \({K_2}\) are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

The ratio for the speed of the electron in the \(3^{ rd }\) orbit of \(He ^{+}\)to the speed of the electron in the \(3^{\text {ad }}\) orbit of hydrogen atom will be

A zener diode of power rating \(1.6\,W\) is to be used as voltage regulator. If the zener diode has a breakdown of \(8\,V\) and it has to regulate voltage fluctuating between \(3\,V\) and \(10 \,V\). The value of resistance \(R_5\) for safe operation of diode will be \(.........\Omega\)

\(64\) identical drops each charged upto potential of \(10\,mV\) are combined to form a bigger dorp. The potential of the bigger drop will be \(..........\,mV\)