The mechanical equivalent of heat $J$ is

Identify the physical parameters from the list given below that have the same dimensions:
$(i)$ Magnetic field $(B)$
$(ii)$ Energy density $(u)$
$(iii)$ Refractive index $(\mu)$
$(iv)$ Young's modulus $(Y)$
$(v)$ Dielectric constant $(K)$

Which of the following pairs does not have the same dimensions?

Which of the following has the same dimensional formula?

In an experiment of measuring the refractive index of a glass slab using a travelling microscope in a physics lab,a student measures the real thickness of the glass slab as $5.25\,mm$ and the apparent thickness of the glass slab as $5.00\,mm$. The travelling microscope has $20$ divisions in $1\,cm$ on the main scale,and $50$ divisions on the Vernier scale are equal to $49$ divisions on the main scale. The estimated uncertainty in the measurement of the refractive index of the slab is $\frac{x}{10} \times 10^{-3}$,where $x$ is $..............$

Match the physical quantities in List-$I$ with their dimensional formulas in terms of mass $(M)$, length $(L)$, time $(T)$ and electric current $(A)$ given in List-$II$.

List-$I$	List-$II$
$(a)$ Torque	$(i)$ $[M^{-1}L^{-2}T^4A^2]$
$(b)$ Gravitational constant	(ii) $[M^1L^2T^{-1}]$
$(c)$ Capacitance	(iii) $[M^{-1}L^3T^{-2}]$
$(d)$ Planck's constant	(iv) $[M^1L^2T^{-2}]$