One main scale division of a vernier caliper is equal to $$\mathrm{m}$$ units. If $$\mathrm{n}^{\text {th }}$$ division of main scale coincides with $$(n+1)^{\text {th }}$$ division of vernier scale, the least count of the vernier caliper is :

If $$\epsilon_{\mathrm{o}}$$ is the permittivity of free space and $$\mathrm{E}$$ is the electric field, then $$\epsilon_{\mathrm{o}} \mathrm{E}^2$$ has the dimensions :

There are 100 divisions on the circular scale of a screw gauge of pitch $$1 \mathrm{~mm}$$. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is :

Least count of a vernier caliper is $$\frac{1}{20 \mathrm{~N}} \mathrm{~cm}$$. The value of one division on the main scale is $$1 \mathrm{~mm}$$. Then the number of divisions of main scale that coincide with $$\mathrm{N}$$ divisions of vernier scale is :