A granite rod of \(60\ cm\) length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is \(2.7 \times 10^3 \) \(kg/m^3\) and its Young's modulus is \(9.27 \times 10^{10}\) \(Pa\) What will be the fundamental frequency of the longitudinal vibrations .... \(kHz\) ?

A fish rising vertically upward with a uniform velocity of \(8\,ms ^{-1}\), observes that a bird is diving vertically downward towards the fish with the velocity of \(12\,ms ^{-1}\). If the refractive index of water is \(\frac{4}{3}\), then the actual velocity of the diving bird to pick the fish, will be \(.......\,ms ^{-1}\).

An oscillating \(LC\) circuit consists of a \(75\,mH\) inductor and a \(1.2\,\mu F\) capacitor. If the maximum charge to the capacitor is \(2.7\,\mu C\). The maximum current in the circuit will be \(...........\,mA\).

The ratio of escape velocity of a planet to the escape velocity of earth will be:Given : Mass of the planet is \(16\) times mass of earth and radius of the planet is \(4\) times the radius of earth.

A current carrying circular loop of radius \(2\) cm with unit normal \(\hat{n} = \dfrac{\hat{k}+\hat{i}}{\sqrt{2}}\) is placed in a magnetic field, \(\vec{B} = B_0(3\hat{i}+2\hat{k})\). If \(B_0 = 4\times 10^{-3}\) T and current \(I=100\sqrt{2}\) A, the torque experienced by the loop is ________ Wb·A. (\(\pi=3.14\))

Two satellites, \(A\) and \(B,\) have masses \(m\) and \(2\,m\) respectively. \(A\) is in a circular orbit of radius \(R,\) and \(B\) is in a circular orbit of radius \(2R\) around the earth. The ratio of their kinetic energies, \(K.E._A / K.E._B ,\) is

If two glass plates have water between them and are separated by very small distance ( see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is \(R\) and surface tension of water is \(T\) then the pressure in water between the plates is lower by

An electric dipole is placed on \({x}\)-axis in proximity to a line charge of linear charge density \(3.0 \times 10^{-6}\, {C} / {m}\). Line charge is placed on \(z-\)axis and positive and negative charge of dipole is at a distance of \(10\, {mm}\) and \(12\, {mm}\) from the origin respectively. If total force of \(4\, {N}\) is exerted on the dipole, find out the amount of positive or negative charge of the dipole.

Given that \(1\,g\) of water in liquid phase has volume \(1\,cm^3\) and in vapour phase \(1671\, cm^3\) at atmospheric pressure and the latent heat of vaporization of water is \(2256\,J/g;\) the change in the internal energy in joules for \(1\,g\) of water at \(373\,K\) when it changes from liquid phase to vapour phase at the same temperature is ....... \(J\)

A \(LCR\) circuit behaves like a damped harmonic oscillator. Comparing it with a physical springmass damped oscillator having damping constant \(\mathrm{b}\), the correct equivalence would be: