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

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 (A) v3 (B) v4 (C) v5 (D) v6

Tardigrade Admin · Accepted Answer

m propto va ρp gc M L0 T0 propto(L T-1)a(M L-3)b(L T-2)c Comparing the powers of M, L, and T and solving, we get b=1, c=-3, a=6 ⇒ m propto v6

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 $ρ$ , and the acceleration due to gravity $g$ . Then $m$ is directly proportional to

$v^{3}$

$v^{4}$

$v^{5}$

$v^{6}$

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

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 ρ, and the acceleration due to gravity g. Then m is directly proportional to

v3

v4

v5

v6