The unit of length convenient on the atomic scale is known as an $\mathring{A}$ and is denoted by $\mathring{A}: 1 \mathring{A} = 10^{-10} \, m$. The size of a hydrogen atom is about $0.5 \mathring{A}$. What is the total atomic volume in $m^{3}$ of a mole of hydrogen atoms?

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 $\ldots . .\, kg\, m ^{-3}$.

State whether the following statements are true or false:
$(a)$ $A$ physical quantity can have units but still be dimensionless.
$(b)$ Impulse and the gradient of energy have the same units.
$(c)$ The absolute error in every measurement is equal to the least count of the measuring instrument.

If $F_1$ and $F_2$ are the relative strengths of the gravitational and weak nuclear forces respectively,then $\frac{F_2}{F_1}$ is nearly

If $\epsilon_0$,$E$,and $t$ represent the free space permittivity,electric field,and time respectively,then the unit of $\frac{\epsilon_0 E}{t}$ will be:

Just as precise measurements are necessary in science,it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain,try to get an upper bound on the quantity):
$(a)$ The total mass of rain-bearing clouds over India during the Monsoon.
$(b)$ The mass of an elephant.
$(c)$ The wind speed during a storm.
$(d)$ The number of strands of hair on your head.
$(e)$ The number of air molecules in your classroom.