An object is falling freely under the gravitational force, its velocity after travelling a distance $h$ is $v$. If $v$ depends upon gravitational acceleration g and distance, find the value of $v^2$ using dimensional analysis.

When the planet Jupiter is at a distance of $824.7$ million kilometres from the earth, its angular diameter is measured to be $35.72"$ of arc. The diameter of Jupiter is $\left(y\times {10}^4\right) \mathrm{km}$. The value of number $y$ to the nearest integer is

(Take $\pi =3.14$)

Write down the no of significant figures in the following:

$0.003{\mathrm{m}}^2$ ,

$0.1250\frac{\mathrm{gm}}{{\mathrm{cm}}^2}$,

 $6.4\times \times {10}^6\mathrm{m}$,

 $1.6\times {10}^{-19}\mathrm{C}$,

 $9.1\times {10}^{-31}\mathrm{kg}$.