The entropy of any system is given by, 
$\mathrm{S}={\alpha }^2\beta \ln \left[\frac{\mu \mathrm{kR}}{\mathrm{J}{\beta }^2}+3\right]$
where $\alpha$ and $\beta$ are the constants. $\mu ,J,k$ and $R$ are number of moles, mechanical equivalent of heat, Boltzmann's constant and gas constant, respectively.
$\left[\text{Take }S=\frac{\mathrm{d}Q}{T}\right]$
Choose the incorrect option from the following:

Three students $S_1,{\mathit{ }\mathit{S}}_2$ and $S_3$ perform an experiment for determining the acceleration due to gravity $\left(g\right)$ using a simple pendulum. They use different lengths of pendulum and record time for different number of oscillations. The observations are as shown in the table.

(Least count of length $=0.1 \mathrm{m}$, least count for time $=0.1 \mathrm{s}$)

If $E_1, E_2$ and $E_3$ are the percentage errors in $g$ for students $1, 2$ and $3$, respectively, then the minimum percentage error is obtained by student no $\underline{ }$ $.$

Student $A$ and student $B$ used two screw gauges of equal pitch and $100$ equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is $0.322 \mathrm{cm}$. The absolute value of the difference between the final circular scale readings observed by the students $A$ and $B$ is _______.

[Figure shows position of reference $O$ when jaws of screw gauge are closed]

Given pitch $=0.1 \mathrm{cm}$.

The force is given in terms of time $t$ and displacement $x$ by the equation $F=A\cos \left(Bx\right)+C\sin \left(Dt\right)$.

The dimensional formula of $\frac{\mathit{A}\mathit{D}}{\mathit{B}}$ is:

$\mathrm{Assertion} A:$ If in five complete rotations of the circular scale, the distance travelled on the main scale of the screw gauge is $5 \mathrm{mm}$ and there are $50$ total divisions on a circular scale, then the least count is $0.001 \mathrm{cm}.$

$\mathrm{Reason} R:$
Least Count $=\frac{\text{ Pitch }}{\text{ Total divisions on circular scale }}$
In the light of the above statements, choose the most appropriate answer from the options given below.

Match List I with List II.

Choose the correct answer from the options given below