The one division of main scale of vernier callipers reads $1 \mathrm{mm}$ and $10$ divisions of Vernier scale is equal to the $9$ divisions on main scale. When the two jaws of the instrument touch each other the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between $4.1 \mathrm{cm}$ and $4.2 \mathrm{cm}$ and $6^{\mathrm{th} }$ Vernier division coincides with a main scale division. The diameter of the bob will be _____ ${10}^{-2} \mathrm{cm}$.

The dimensions of $\left(\frac{B^2}{{\mu }_0}\right)$ will be

(if ${\mu }_0$: permeability of free space and $B :$magnetic field)

Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R)

Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension $\left(S\right)$, if density of the liquid is $\rho$ and radius of the drop is $r$, then $T=K\sqrt{\frac{\rho r^3}{S^{{\displaystyle \frac{3}{2}}}}}$ is dimensionally correct, where $K$ is dimensionless.

Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below.

In an experiment to find out the diameter of wire using screw gauge, the following observation were noted:

(a) Screw moves $0.5 \mathrm{mm}$ on main scale in one complete rotation
(b) Total divisions on circular scale $=50$
(c) Main scale reading is $2.5 \mathrm{mm}$
(d) ${45}^{\mathrm{th}}$${ }^{}$ division of circular scale is in the pitch line
(e) Instrument has $0.03 \mathrm{mm}$ negative error Then the diameter of wire is :

Match List I with List II