Density of a liquid in $CGS$ system is $0.625 g/c{m^3}$. What is its magnitude in $SI $ system
$0.625$
$0.0625$
$0.00625$
$625$
Density of a liquid in $CGS$ system is $0.625 g/c{m^3}$. What is its magnitude in $SI $ system
$CGS$ $SI$
${N_1}{U_1} = {N_2}{U_2}$
${N_1}\left[ {{M_1}L_1^{ - 3}} \right] = {N_2}\left[ {{M_2}L_2^{ - 3}} \right]$
$\therefore $ ${N_2} = {N_1}\left[ {\frac{{{M_1}}}{{{M_2}}}} \right] \times {\left[ {\frac{{{L_1}}}{{{L_2}}}} \right]^{ - 3}}$ $ = 0.625\left[ {\frac{{1g}}{{1kg}}} \right] \times {\left[ {\frac{{1cm}}{{1m}}} \right]^{ - 3}}$
$ = 0.625 \times {10^{ - 3}} \times {10^6} = 625$
${N_1}{U_1} = {N_2}{U_2}$
${N_1}\left[ {{M_1}L_1^{ - 3}} \right] = {N_2}\left[ {{M_2}L_2^{ - 3}} \right]$
$\therefore $ ${N_2} = {N_1}\left[ {\frac{{{M_1}}}{{{M_2}}}} \right] \times {\left[ {\frac{{{L_1}}}{{{L_2}}}} \right]^{ - 3}}$ $ = 0.625\left[ {\frac{{1g}}{{1kg}}} \right] \times {\left[ {\frac{{1cm}}{{1m}}} \right]^{ - 3}}$
$ = 0.625 \times {10^{ - 3}} \times {10^6} = 625$