A wooden block floats with $\frac{3}{5}$ of its volume submerged in a tank of water. If a denser liquid is poured into the tank, the wooden block floats with half its volume in the liquid and the remaining half in water. The relative density of the liquid is:

A particle starts from rest and moves along the x -axis with a velocity that varies as $\mathrm{v}=\sqrt{100+4 x} \mathrm{~ms}^{-1}$. The acceleration of the particle is:

If E is the amplitude of the electric field of the waves starting from the slits in a double slit experiment and $\theta$ is the phase difference between the waves reaching a point on the screen, the ratio of the amplitude of the resultant electric field at that point on the screen to the amplitude at one of the slits is

Two simple harmonic motions are represented by equations $y_1=0.5 \sin \left[200 \pi \mathrm{t}+\frac{\pi}{3}\right]$ and $y_1=0.5 \cos \pi \mathrm{t}$. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is :