The density of a material in $CGS$ system of units is $4 \, g \, cm^{-3}$. In a system of units in which the unit of length is $10 \, cm$ and the unit of mass is $100 \, g$,the value of the density of the material will be:

Which physical quantities have the same dimension?

The fundamental unit which has the same power in the dimensional formula of surface tension and viscosity is

Match the following (Take the relative strength of the strongest fundamental forces in nature as $1$):

$I$ (Fundamental forces in nature)	$II$ (Relative strength)
$(A)$ Strong nuclear force	$(e)$ $10^{-2}$
$(B)$ Weak nuclear force	$(f)$ $1$
$(C)$ Electromagnetic force	$(g)$ $10^{10}$
$(D)$ Gravitational force	$(h)$ $10^{-13}$
	$(i)$ $10^{-39}$

The correct match is:

Fill in the blanks:
$(a)$ $1 \ \text{Joule} = \dots \ \text{erg}$
$(b)$ $1 \ \text{eV} = \dots \ \text{Joule}$
$(c)$ $1 \ \text{kWh} = \dots \ \text{Joule}$

The maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its rotational kinetic energy $(K = \frac{1}{2} I \omega^{2})$. (in $\%$)