Question

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

• A. ${10}^5$
• B. ${10}^3$
• C. ${10}^7$
• D. ${10}^{-5}$

Answer 1

Answer: (A)

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