Question

The density of mercury is 13.6 gram per centimetre cube now convert into mks method by dimensional method

Answer 1

we know, dimensional formula of density = $[ML^{-3}]$

here we should use the formula,

$\bf{d_1[M_1L_1^{-3}]=d_2[M_2L_2^{-3}]}$

where we assumed, $d_1$ is the density of mercury in CGS system and $d_2$ is the density of mercury in mks system.

then, now, $d_1$ = 13.6 $M_1=1g=10^{-3}kg$

$L_1=1cm=10^{-2}m$

$M_2=1kg,L_2=1m$

so, $d_2=d_1\frac{[M_1L_1^{-3}]}{[M_2L_2^{-3}]}$

= 13.6$\left[\frac{M_1}{M_2}\right]\left[\frac{L_1}{L_2}\right]^{-3}$

= $\left[\frac{10^{-3}kg}{1kg}\right]\left[\frac{10^{-2}m}{1m}\right]^{-3}$

= 13.6 × 10^-3 × (10^-2)^-3

= 13.6 × 10^-3 × 10^6

= 13.6 × 10³

hence, density of mercury in mks unit is 13.6 × 10³ kg/m³