Stokes' law states that the viscous drag forc | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The given equation is $\frac{V}{t} = k \left( \frac{p}{l} \right)^a \eta^b r^c$.The dimensions of the quantities are:$[V/t] = [L^3 T^{-1}]$$[p/l]

Vedclass · Accepted Answer

$a=1, b=-1, c=4$

Vedclass · Answer

(A) The given equation is $\frac{V}{t} = k \left( \frac{p}{l} \right)^a \eta^b r^c$.The dimensions of the quantities are:$[V/t] = [L^3 T^{-1}]$$[p/l] = [M L^{-1} T^{-2} / L] = [M L^{-2} T^{-2}]$$[\eta] = [M L^{-1} T^{-1}]$$[r] = [L]$Substituting these into the equation:$[L^3 T^{-1}] = [M L^{-2} T^{-2}]^a [M L^{-1} T^{-1}]^b [L]^c$$[L^3 T^{-1}] = M^{a+b} L^{-2a-b+c} T^{-2a-b}$Equating the powers of $M, L,$ and $T$ on both sides:For $M$: $a + b = 0 \Rightarrow b = -a$For $T$: $-2a - b = -1$Substituting $b = -a$ into the $T$ equation: $-2a - (-a) = -1 \Rightarrow -a = -1 \Rightarrow a = 1$.Since $b = -a$,we get $b = -1$.For $L$: $-2a - b + c = 3$Substituting $a = 1$ and $b = -1$: $-2(1) - (-1) + c = 3 \Rightarrow -2 + 1 + c = 3 \Rightarrow -1 + c = 3 \Rightarrow c = 4$.Thus,the values are $a=1, b=-1, c=4$.

Similar Questions

In a practical unit system,if the unit of mass becomes double and that of time becomes half,then $8 \text{ joule}$ will be equal to .............. unit of work.

Planck's constant $h$,speed of light $c$,and gravitational constant $G$ are used to form a unit of length $L$ and a unit of mass $M$. Then the correct option$(s)$ is(are):
$(A)$ $M \propto \sqrt{c}$
$(B)$ $M \propto \sqrt{G}$
$(C)$ $L \propto \sqrt{h}$
$(D)$ $L \propto \sqrt{G}$

The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$,where $P$ is the pressure difference and $v$ is the velocity. Then,the relation between $x$ and $y$ is

State the principle of homogeneity of dimensions.

The displacement $y$ of a particle at a distance $x$ at time $t$ for a transverse wave is given by $y = a \sin(bt - cx)$,where $a, b,$ and $c$ are constants. The dimensions of $b/c$ are the same as those of:

Vedclass Test Series

Exam Paper Generator

Online Exam Module