1. Tardigrade
  2. Question
  3. Physics
  4. 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 ρ, and the acceleration due to gravity g. Then m is directly proportional to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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

Physical World, Units and Measurements

Solution:

$m \propto v^{a} \rho^{p} g^{c}$
$M L^{0} T^{0} \propto\left(L T^{-1}\right)^{a}\left(M L^{-3}\right)^{b}\left(L T^{-2}\right)^{c}$
Comparing the powers of $M, L$, and $T$ and solving,
we get $b=1, c=-3, a=6 $
$\Rightarrow m \propto v^{6}$