The pitch of an error free screw gauge is $$1 \mathrm{~mm}$$ and there are 100 divisions on the circular scale. While measuring the diameter of a thick wire, the pitch scale reads $$1 \mathrm{~mm}$$ and $$63^{\text {rd }}$$ division on the circular scale coincides with the reference line. The diameter of the wire is:

The potential energy of a particle moving along $$x$$-direction varies as $$V=\frac{A x^2}{\sqrt{x}+B}$$. The dimensions of $$\frac{A^2}{B}$$ are:

In a vernier callipers, $$(N+1)$$ divisions of vernier scale coincide with $$N$$ divisions of main scale. If $$1 \mathrm{~MSD}$$ represents $$0.1 \mathrm{~mm}$$, the vernier constant (in $$\mathrm{cm}$$) is:

The quantities which have the same dimensions as those of solid angle are: