The charges $$2 \mathrm{q},-\mathrm{q},-\mathrm{q}$$ are located at the vertices of an equilateral triangle. At the circumcentre of the triangle

The magnetic field at a point $$\mathrm{P}$$ situated at perpendicular distance '$$R$$' from a long straight wire carrying a current of $$12 \mathrm{~A}$$ is $$3 \times 10^{-5} \mathrm{~Wb} / \mathrm{m}^2$$. The value of '$$\mathrm{R}$$' in $$\mathrm{mm}$$ is $$\left[\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}\right]$$

A particle at rest starts moving with constant angular acceleration $$4 ~\mathrm{rad} / \mathrm{s}^2$$ in circular path. At what time the magnitudes of its tangential acceleration and centrifugal acceleration will be equal?

If the end correction of an open pipe is $$0.8 \mathrm{~cm}$$, then the inner radius of that pipe is