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Question

Physics Question on Dimensional Analysis

If 'muscle times speed equals power' what is the ratio of the SISI unit and the CGSCGS unit of muscle?

A

10510^{5}

B

10310^{3}

C

10710^{7}

D

10−510^{-5}

Answer

10510^{5}

Explanation

Solution

Muscle ×\times speed == power
∴\therefore Muscle = power  speed = work  time × speed =\frac{\text { power }}{\text { speed }}=\frac{\text { work }}{\text { time } \times \text { speed }}
=[ML2T−2][T][LT−1]=[MLT−2]=\frac{\left[M L^{2} T^{-2}\right]}{[T]\left[L T^{-1}\right]}=\left[M L T^{-2}\right]
== mass ×\times acceleration == force
Hence,  SI unit of force  CGS unit of force \frac{\text { SI unit of force }}{\text { CGS unit of force }}
=kg×m×s−2g×cm×s−2=\frac{k g \times m \times s^{-2}}{g \times c m \times s^{-2}}
=103×102=105=10^{3} \times 10^{2}=10^{5}