Physics And Measurement Question 265
Question: Assuming that the mass m of the largest stone that can be moved by a flowing river depends upon the velocity v of the water, its density $ \rho $ and the acceleration due to gravity g. Then m is directly proportional to:
Options:
A) $ {{\nu }^{3}} $
B) $ {{\nu }^{4}} $
C) $ {{\nu }^{5}} $
D) $ {{\nu }^{6}} $
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Answer:
Correct Answer: D
Solution:
[d] $ m\propto v^{x}{{\rho }^{y}}g^{z} $
$ M\equiv {{[L{{T}^{-1}}]}^{x}}{{[M{{L}^{-3}}]}^{y}}{{[L{{T}^{-2}}]}^{z}} $
$ M^{1}L^{0}T^{0}=M^{y}{{L}^{x-3y+z}}{{T}^{-x-2z}} $
$ y=1.x-3y+z=0,-x-2z=0 $
Solving above equations $ x-3-\frac{x}{2}=0\Rightarrow \frac{x}{2}=3\Rightarrow x=6 $
