Match List-$I$ with List-$II$:

$LIST$-$I$	$LIST$-$II$
$(A)$ Surface tension	$(I)$ $kg m^{-1} s^{-1}$
$(B)$ Pressure	$(II)$ $kg m s^{-1}$
$(C)$ Viscosity	$(III)$ $kg m^{-1} s^{-2}$
$(D)$ Impulse	$(IV)$ $kg s^{-2}$

Choose the correct answer from the options given below:

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 $..............$

Fill in the blanks:
$(a)$ The volume of a cube of side $1\; cm$ is equal to $\ldots \ldots\, m ^{3}$
$(b)$ The surface area of a solid cylinder of radius $2.0 \;cm$ and height $10.0\; cm$ is equal to $\ldots(mm)^{2}$
$(c)$ $A$ vehicle moving with a speed of $18\; km\, h ^{-1}$ covers $\ldots ..m$ in $1\; s$
$(d)$ The relative density of lead is $11.3$. Its density is $\ldots ..\, g\, cm ^{-3}$ or $\ldots . .\, kg\, m ^{-3}$.

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 $\%$)

Identify the physical quantity that has the unit $N\,m^{-1}\,s^{-2}$.

The diameter of a wire measured by a screw gauge of least count $0.001 \text{ cm}$ is $0.08 \text{ cm}$. The length measured by a scale of least count $0.1 \text{ cm}$ is $150 \text{ cm}$. When a weight of $100 \text{ N}$ is applied to the wire, the extension in length is $0.5 \text{ cm}$, measured by a micrometer of least count $0.001 \text{ cm}$. The error in the measured Young's modulus is $\alpha \times 10^9 \text{ N/m}^2$. The value of $\alpha$ is . . . . . . . (Ignore the contribution of the load to Young's modulus error calculation)