Electric charge is transferred to an irregular metallic disk as shown in the figure. If $\sigma_1$, $\sigma_2$, $\sigma_3$ and $\sigma_4$ are charge densities at given points then, choose the correct answer from the options given below:

A. $\sigma_1>\sigma_3 ; \sigma_2=\sigma_4$

B. $\sigma_1>\sigma_2 ; \sigma_3>\sigma_4$

C. $\sigma_1>\sigma_3>\sigma_2=\sigma_4$

D. $\sigma_1<\sigma_3<\sigma_2=\sigma_4$

E. $\sigma_1=\sigma_2=\sigma_3=\sigma_4$

An infinitely long wire has uniform linear charge density $\lambda = 2 \text{ nC/m}$. The net flux through a Gaussian cube of side length $\sqrt{3}$ cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $x \text{ Nm}^2\text{C}^{-1}$, where $x$ is:

[Neglect any edge effects and use $\frac{1}{4\pi \epsilon_0} = 9 \times 10^9$ SI units]

A body of mass 2 kg moving with velocity of $ \vec{v}_{in} = 3 \hat{i} + 4 \hat{j} \text{ ms}^{-1} $ enters into a constant force field of 6N directed along positive z-axis. If the body remains in the field for a period of $ \frac{5}{3} $ seconds, then velocity of the body when it emerges from force field is.

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be