Let $L, R, C$ and $V$ represent inductance,resistance,capacitance,and voltage,respectively. The dimension of $\frac{L}{RCV}$ in $SI$ units will be:

Fill in the blanks by suitable conversion of units:
$(a)$ $1\; kg\; m^{2}\; s^{-2} = \ldots\; g\; cm^{2}\; s^{-2}$
$(b)$ $1\; m = \ldots\; ly$
$(c)$ $3.0\; m\; s^{-2} = \ldots\; km\; h^{-2}$
$(d)$ $G = 6.67 \times 10^{-11}\; N\; m^{2}\; kg^{-2} = \ldots\; cm^{3}\; s^{-2}\; g^{-1}$

Dimensions of the quantity $\frac{p}{\varepsilon_0 \mu_0}$,where $p$ is the pressure,$\varepsilon_0$ is the electric permittivity of free space,and $\mu_0$ is the permeability of free space,will be:

State whether the following statements are true or false:
$(a)$ $A$ dimensionally incorrect equation can be correct.
$(b)$ $1 \ AU = 9.46 \times 10^{15} \ m$
$(c)$ The dimensional formula of force and stress are the same.
$(d)$ The dimensions of a physical quantity are different in different systems of units.

The length of a cylinder is measured with a meter rod having a least count of $0.1 \, cm$. Its diameter is measured with vernier calipers having a least count of $0.01 \, cm$. Given that the length is $5.0 \, cm$ and the radius is $2.0 \, cm$,the percentage error in the calculated value of the volume will be ......... $\%$

$M{L^{ - 1}}{T^{ - 2}}$ represents: