If the present units of length,time,and mass $(m, s, kg)$ are changed to $100 \; m, 100 \; s, 0.1 \; kg$,then:

$A$ wave pulse can travel along a tense string like a violin string. $A$ series of experiments showed that the wave velocity $V$ of a pulse depends on the following quantities: the tension $T$ of the string,the cross-sectional area $A$ of the string,and the density $\rho$ (mass per unit volume) of the string. Obtain an expression for $V$ in terms of $T$,$A$,and $\rho$ using dimensional analysis.

If force $(F)$,length $(L)$,and time $(T)$ are assumed to be fundamental units,then the dimensional formula of mass will be:

The value of gravitational acceleration in the $C.G.S.$ system is $980 \; cm/s^2$. Find the value of $g$ in the $M.K.S.$ system.

Planck's constant $h$,speed of light $c$,and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are):
$(A)$ $M \propto \sqrt{c}$
$(B)$ $M \propto \sqrt{G}$
$(C)$ $L \propto \sqrt{h}$
$(D)$ $L \propto \sqrt{G}$

The entropy of any system is given by
$S = \alpha^{2} \beta \ln \left[\frac{\mu k R}{J \beta^{2}} + 3\right]$
Where $\alpha$ and $\beta$ are constants. $\mu, J, k$ and $R$ are the number of moles,mechanical equivalent of heat,Boltzmann constant,and gas constant respectively. [Take $S = \frac{dQ}{T}$].
Choose the incorrect option from the following: