A whistling train approaches a junction. An observer standing at the junction observes the frequency to be 2.2 kHz and 1.8 kHz of the approaching and the receding train. Find the speed of the train (speed of sound = 300 m/s).

A conducting liquid bubble of radius $$a$$ and thickness $$t(t < < a)$$ is charged to potential V. If the bubble collapses to a droplet, find the potential on the droplet.

The potential energy of a particle of mass m is given by

$$\mathrm{U}(x)=\left\{\begin{array}{cc}\mathrm{E}_{0} & 0 \leq x \leq 1 \\ 0 & x>1\end{array}\right.$$

$$\lambda_{1}$$ and $$\lambda_{2}$$ are the de Broglie wavelengths of the particle, when $$0 \leq x \leq 1$$ and $$x > 1$$, respectively. If the total energy of particle is $$2 \mathrm{E}_{0}$$, find $$\frac{\lambda_{1}}{\lambda_{2}}$$.

A U-tube is rotated about one of its limbs with an angular velocity $$\omega$$. Find the difference in height $$\mathrm{H}$$ of the liquid (density $$\rho$$ ) level, where the diameter of the tube is $$d < <\mathrm{L}$$.