In finding the electric field using Gauss Law the formula $$\left| {\overrightarrow E } \right| = {{{q_{enc}}} \over {{\varepsilon _0}\left| A \right|}}$$ is applicable. In the formula $${{\varepsilon _0}}$$ is permittivity of free space, A is the area of Gaussian surface and q_enc is charge enclosed by the Gaussian surface. The equation can be used in which of the following situation?

The graph which depicts the results of Rutherford gold foil experiment with $$\alpha $$-particales is :
$$\theta $$ : Scattering angle
Y : Number of scattered $$\alpha $$-particles detected (Plots are schematic and not to scale)

A particle is moving along the x-axis with its coordinate with the time 't' given be
x(t) = 10 + 8t – 3t². Another particle is moving the y-axis with its coordinate as a function of time given by y(t) = 5 – 8t³.
At t = 1s, the speed of the second particle as measured in the frame of the first particle is given as $$\sqrt v $$. Then v (in m/s) is ______.

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.