The temperature of an ideal gas is increased from 100 K to 400 K . If ' $x$ ' is the R.M.S. velocity of its molecules at 100 K , it becomes

What is the phase difference between the flux linked with a coil rotating in a uniform magnetic field and the induced e.m.f. produced in it?

A pendulum bob has a speed $4 \mathrm{~m} / \mathrm{s}$ at its lowest position. The pendulum is 1 m long. When the length of the string makes an angle of $60^{\circ}$ with the vertical, the speed of the bob at that position is (acceleration due to gravity, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$, $\cos 60^{\circ}=0.5$ )

A vehicle starts from rest and accelerates along straight path at $2 \mathrm{~m} / \mathrm{s}^2$. At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the siren at $94 \%$ of its value when the vehicle was at rest?

(speed of sound $=220 \mathrm{~m} / \mathrm{s}$ )