Physics And Measurement Question 207

Question: In a new system of units, the fundamental quantities mass, length and time are replaced by acceleration ‘a’, density $ ‘\rho ’ $ and frequency $ f $ . The dimensional formula for force in this system is

Options:

A) $ [\rho a^{4}f] $

B) $ [\rho a^{4}{{f}^{-6}}] $

C) $ [{{\rho }^{-1}}{{a}^{-4}}f^{6}] $

D) $ [{{\rho }^{-1}}{{a}^{-4}}f^{6}] $

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Answer:

Correct Answer: B

Solution:

[b] $ F=ma=\rho $ volume a To write volume in terms of aand f Volumes

$ =L^{3}{{( \frac{L}{T^{2}} )}^{3}}T^{6}=a^{3}{{f}^{-6}} $

$ \therefore F=\rho a^{4}{{f}^{-6}} $



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