A coil is placed perpendicular to a magnetic field of 5000 T . When the field is changed to 3000 T in 2 s , an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m , then the number of turns in the coil is _______.

The temperature of equal masses of three different liquids \({x}, {y}\) and \({z}\) are \(10^{\circ} {C}, 20^{\circ} {C}\) and \(30^{\circ} {C}\) respectively. The temperature of mixture when \({x}\) is mixed with \({y}\) is \(16^{\circ} {C}\) and that when \({y}\) is mixed with \(z\) is \(26^{\circ} {C}\). The temperature of mixture when \(x\) and \(z\) are mixed will be ...... \(^{\circ} {C}\)

Two bodies of masses \(m_{1}=5\,kg\) and \(m _{2}=3\,kg\) are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass \(m _{1}\) will be\(....N\) [Take \(g=10\,ms ^{-2}\) ]

A particle is moving with speed \(v= b\sqrt x\) along positive \(x-\) axis. Calculate the speed of the particle at time \(t = \tau\) (assume that the particle is at origin at \(t = 0\) ).

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is _______.

On a linear temperature scale \(Y\), water freezes at \(- 160^o\, Y\) and boils at \(- 50^o\, Y\). On this \(Y\) scale , a temperature of \(340\, K\) would be read as........ \(^oY\)  ( water freezes at \(273\, K\) and boils at \(373\, K\))

The magnetic moment of an electron \((e)\) revolving in an orbit around nucleus with an orbital angular momentum is given by :

Consider a solid sphere of radius \(\mathrm{R}\) and mass density \(\rho(\mathrm{r})=\rho_{0}\left(1-\frac{\mathrm{r}^{2}}{\mathrm{R}^{2}}\right),  0<\mathrm{r} \leq \mathrm{R} .\) The minimum density of a liquid in which it will float is

To mop-clean a floor, a cleaning machine presses a circular mop of radius \(R\) vertically down with a total force \(F\) and rotates it with a constant angular speed about its axis. If the force \(F\) is distributed uniformly over the mop and the floor is \(\mu \), the torque, applied by the machine on the mop is

For the \(LCR\) circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor \(C '\) , when joined with the capacitor \(C\) present in the circuit , makes the power factor of the circuit unity. The capacitor \(C'\), must have been connected in

A parallel plate capacitor has a capacitance \(\mathrm{C}=200 \mathrm{pF}\). It is connected to \(230 \mathrm{~V}\) ac supply with an angular frequency \(300 \mathrm{rad} / \mathrm{s}\). The \(\mathrm{rms}\) value of conduction current in the circuit and displacement current in the capacitor respectively are _______.