Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at $x=0.1 \mathrm{~cm}$ when the jaws of Vernier callipers are closed. If the main scale reading for the diameter is $M=5 \mathrm{~cm}$ and the number of coinciding vernier division is 8 , the measured diameter after zero error correction, is

In an electrical circuit, the voltage is measured as $$V=(200 \pm 4)$$ volt and the current is measured as $$I=(20 \pm 0.2)$$ A. The value of the resistance is:

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: