A stone tied to \(180 cm\) long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is \(\frac{1936}{ x }\,ms ^{-2}\). The value of \(x.........\left(\text { Take } \pi=\frac{22}{7}\right)\)

In the given circuit if the power rating of Zener diode is \(10 \mathrm{~mW}\), the value of series resistance \(R_s\) to regulate the input unregulated supply is _______.

Two factories are sounding their sirens at \(800\, Hz\) . A man goes from one factory to other at a speed of \(2\,m/s\). The velocity of sound is \(320\, m/s\). The number of beats heard by the person in one second will be

Two different wires having lengths \(L _{1}\) and \(L _{2}\) and respective temperature coefficient of linear expansion \(\alpha_{1}\) and \(\alpha_{2},\) are joined end-to-end. Then the effective temperature coefficient of linear expansion is

A linearly polarized electromagnetic wave in vacuum is \(E=3.1 \cos \left[(1.8) z-\left(5.4 \times 10^{6}\right) {t}\right] \hat{\text { i }}\, {N} / {C}\) is incident normally on a perfectly reflecting wall at \(z=a\). Choose the correct option

The velocity of water in a river is \(18\, km/h\) near the surface. If the river is \(5\, m\) deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water \(= 10^{-2}\,,poise\)

A uniformly thick wheel with moment of inertia \(I\) and radius \(R\) is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\left(\mathrm{m}_{1}>\mathrm{m}_{2}\right)\) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when \(\mathrm{m}_{1}\) descents by a distance \(h\) is

A rod of length \(L\) has non-uniform linear mass density given by \(\rho(\mathrm{x})=\mathrm{a}+\mathrm{b}\left(\frac{\mathrm{x}}{\mathrm{L}}\right)^{2},\) where \(a\) and \(\mathrm{b}\) are constants and \(0 \leq \mathrm{x} \leq \mathrm{L}\). The value of \(\mathrm{x}\) for the centre of mass of the rod is at

The de Broglie wavelength of a proton and \(\alpha\) -particle are equal. The ratio of their velocities is ...... .

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from \(440\, Hz\) to \(480 \,Hz ,\) when it gets reflected from the wall. If the speed of sound in air is \(345 \,m / s ,\) then the speed of the car is \(.......km/hr\)