In free space, a particle A of charge 1$$\mu $$C is held fixed at a point P. Another particle B of the same charge and mass 4$$\mu $$g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is : $$\left[ {Take\,{1 \over {4\pi { \in _0}}} = 9 \times {{10}^9}N{m^2}{C^{ - 2}}} \right]$$

In the formula X = 5YZ² , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

A bullet of mass 20 g has an initial speed of 1 ms^–1 , just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of 2.5 × 10^–2 N, the speed of the bullet after emerging from the other side of the wall is close to :

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6 V and the load resistance is, R_L = 4k$$\Omega $$. The series resistance of the circuit is R_i = 1 k$$\Omega $$. If the battery voltage V_B varies from 8 V to 16 V, what are the minimum and maximum values of the current through Zener diode?