The pair having the same dimensions is

Which of the following pairs of quantities do not have the same dimensions?

The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge,whose pitch is $0.5 \ mm$ and there are $50$ divisions on the circular scale. The reading on the main scale is $2.5 \ mm$ and that on the circular scale is $20$ divisions. If the measured mass of the ball has a relative error of $2 \%$,the relative percentage error in the density is (in $\%$)

If we use permittivity $\varepsilon$,resistance $R$,gravitational constant $G$,and voltage $V$ as fundamental physical quantities,then:

To determine the Young's modulus of a wire,the formula is $Y = \frac{FL}{A\Delta L}$,where $L$ is the length,$A$ is the area of cross-section of the wire,and $\Delta L$ is the change in length of the wire when stretched with a force $F$. The conversion factor to change the unit of Young's modulus from $CGS$ to $MKS$ system is $x \times 10^{-1} \ N/m^2$. Find the value of $x$.

Match List-$I$ and List-$II$:

List-$I$	List-$II$
$A$. Young's Modulus $(Y)$	$I$. $[M L^{-1} T^{-1}]$
$B$. Co-efficient of Viscosity $(\eta)$	$II$. $[M L^2 T^{-1}]$
$C$. Planck's Constant $(h)$	$III$. $[M L^{-1} T^{-2}]$
$D$. Work Function $(\varphi)$	$IV$. $[M L^2 T^{-2}]$

Choose the correct answer from the options given below: