A weightless thread can bear tension up to 3.7 kg wt. A stone of mass 500 gram is tied to it and revolved in circular path of radius 4 m in vertical plane. Maximum angular velocity of the stone will be (acceleration due to gravity, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

Water is flowing steadily in a river. A and B are the two layers of water at heights 40 cm and 90 cm from the bottom. The velocity of the layer A is $12 \mathrm{~cm} / \mathrm{s}$. The velocity of the layer B is

A progressive wave of frequency 400 Hz is travelling with velocity $336 \mathrm{~m} / \mathrm{s}$. How far apart are the two points on a wave which are $60^{\circ}$ out of phase?

The magnetic flux through a coil is $4 \times 10^{-4} \mathrm{~Wb}$ at time $t=0$. It reduces to $30 \%$ of its original value in time $t$ second. If e.m.f. induced in the coil is 0.56 mV then the value of $t$ is