Assume that the largest stone of mass $^{'} m^{'}$ that can be moved by a flowing river depends upon the velocity of flow $v$ , the density $d$ & the acceleration due to gravity $g$ . If $^{'} m^{'}$ varies as the $K^{t h}$ power of the velocity of flow, then find the value of $K$ .

Open in App

Solution

$m α [v]^{k} [d]^{x} [g]^{y}$
$[M^{1} L^{0} T^{0}] = [L T^{- 1}]^{k} [M L^{- 3}]^{x} [L T^{- 2}]^{y}$
$\Rightarrow x = 1, k = - 3 x + y, - k - 2 y = 0$
$\Rightarrow x = 1, y = - 3, a n d K = 6$

Suggest Corrections

Similar questions

Q. Assume that the mass

(m)

of the largest stone that can be moved by the flowing river depends only upon the velocity

v

and the density

ρ

of the water, along with the acceleration due to gravity

g

. Show that

m

varies with sixth power of the velocity of the flow.

Assuming that the mass 'M' of the largest stone that can be moved by a flowing river depends upon velocity'v',density of water(p) and on acceleration due to gravity 'g'.show that mass'M' varies with the sixth power of the velocity of flow.

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

Q. Assume that the mass M of the largest stone that can be moved by a flowing river depends upon the velocity v, the density of water d and the acceleration due to gravity g. Deduce the relationship between these quantities by dimensional analysis method.

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

Join BYJU'S Learning Program

Assume that the largest stone of mass ′m′ that can be moved by a flowing river depends upon the velocity of flow v, the density d & the acceleration due to gravity g. If ′m′ varies as the Kth power of the velocity of flow, then find the value of K.

mα[v]k[d]x[g]y[M1L0T0]=[LT−1]k[ML−3]x[LT−2]y⇒x=1,k=−3x+y,−k−2y=0⇒x=1,y=−3,andK=6

Assume that the largest stone of mass $^{'} m^{'}$ that can be moved by a flowing river depends upon the velocity of flow $v$ , the density $d$ & the acceleration due to gravity $g$ . If $^{'} m^{'}$ varies as the $K^{t h}$ power of the velocity of flow, then find the value of $K$ .

$m α [v]^{k} [d]^{x} [g]^{y}$
$[M^{1} L^{0} T^{0}] = [L T^{- 1}]^{k} [M L^{- 3}]^{x} [L T^{- 2}]^{y}$
$\Rightarrow x = 1, k = - 3 x + y, - k - 2 y = 0$
$\Rightarrow x = 1, y = - 3, a n d K = 6$