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}} $
