The displacement of a damped oscillator is $x(t)=\exp (-0.2 t) \cos (3.2 t+\phi)$, where $t$ is time in second The time requirement for the amplitude of the oscillator to become $\frac{1}{e^{1.2}}$ times its initial amplitude is

Maximum height reached by a rocket fired with a speed equal to $50 \%$ of the escape speed from the surface of the earth is ( $R=$ Radius of the earth)

If the work done in stretching a wire by 1 min is 2 J . The work necessary for stretching another wire of satrs material but with double radius of cross-section and half the length by 1 mm is

If $S_1, S_2$ and $S_3$ are the tensions at liquid-air, solid-air and solid-liquid interfaces respectively and $\theta$ is the angle of contact at the solid-liquid interface, then