If the unit of force is $100\,N$,unit of length is $10\,m$ and unit of time is $100\,s$,what is the unit of mass in this system of units?

Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$,moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$,is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$,length $l$ and pressure difference of $p$ across its two ends,then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$,where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are

Which of the following equations is dimensionally incorrect?
Where $t=$ time,$h=$ height,$s=$ surface tension,$\theta=$ angle,$\rho=$ density,$a, r=$ radius,$g=$ acceleration due to gravity,$v=$ volume,$p=$ pressure,$W=$ work done,$\Gamma=$ torque,$\varepsilon=$ permittivity,$E=$ electric field,$J=$ current density,$L=$ length.

The position of a particle at time $t$ is given by the relation $x(t) = \left( \frac{v_0}{\alpha} \right) (1 - e^{-\alpha t})$,where $v_0$ is a constant and $\alpha > 0$. The dimensions of $v_0$ and $\alpha$ are respectively:

The characteristic distance at which quantum gravitational effects are significant,the Planck length,can be determined from a suitable combination of the fundamental physical constants $G, h$ and $c$. Which of the following correctly gives the Planck length?

Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.