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  4. If muscle times speed equals power, what is the ratio of the SI unit and the CGS unit of muscle?

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Q. If muscle times speed equals power, what is the ratio of the SI unit and the CGS unit of muscle?

ManipalManipal 2008Physical World, Units and Measurements

Solution:

Muscle $\times$ speed $=$ power
$ \therefore $ Muscle $=\frac{\text { power }}{\text { speed }}=\frac{\text { work }}{\text { time } \times \text { speed }}$
$=\frac{\left[ ML ^{2} T ^{-2}\right]}{[ T ]\left[ LT ^{-1}\right]}=\left[ MLT ^{-2}\right] $
$=$ mass $ \times$ acceleration $=$ force
Hence, $ \frac{\text { SI unit of force }}{\text { CGS unit of force }}=\frac{ kg \times m \times s ^{-2}}{ g \times cm \times s ^{-2}}$
$=10^{3} \times 10^{2}=10^{5}$