What could be a correct expression for the sp | vedclass

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

Question

(A) To determine the correct expression,we use dimensional analysis.The dimension of speed $v$ is $[LT^{-1}]$.For option $(A)$,the dimension of $\sqrt

Vedclass · Accepted Answer

$\sqrt{g\lambda}$

Vedclass · Answer

(A) To determine the correct expression,we use dimensional analysis.The dimension of speed $v$ is $[LT^{-1}]$.For option $(A)$,the dimension of $\sqrt{g\lambda}$ is $\sqrt{[LT^{-2}] \cdot [L]} = \sqrt{[L^2T^{-2}]} = [LT^{-1}]$,which matches the dimension of speed.For option $(B)$,the dimension of $\sqrt{g/h}$ is $\sqrt{[LT^{-2}] / [L]} = \sqrt{[T^{-2}]} = [T^{-1}]$,which is incorrect.For option $(C)$,the dimension of $\sqrt{\rho gh}$ is $\sqrt{[ML^{-3}] \cdot [LT^{-2}] \cdot [L]} = \sqrt{[MT^{-2}]}$,which is incorrect.For option $(D)$,the dimension of $\sqrt{g/\rho}$ is $\sqrt{[LT^{-2}] / [ML^{-3}]} = \sqrt{[M^{-1}L^4T^{-2}]}$,which is incorrect.Therefore,the only dimensionally consistent expression is $\sqrt{g\lambda}$.

What could be a correct expression for the speed of ocean waves in terms of its wavelength $\lambda$,the depth $h$ of the ocean,the density $\rho$ of sea water,and the acceleration of free fall $g$?

Similar Questions

The electric field in a certain region is given by the formula $\vec{E} = (\frac{K}{x^3}) \hat{i}$. What is the dimensional formula of $K$?

In a new system of units,energy $(E)$,density $(d)$,and power $(P)$ are taken as fundamental units. Then the dimensional formula of the universal gravitational constant $G$ will be .......

If the acceleration due to gravity is $10\,m/s^2$ and the units of length and time are changed to kilometer and hour respectively,the numerical value of the acceleration is

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 equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure,$V$ is the volume,$T$ is the absolute temperature and $a, b, R$ are constants. The dimensions of $a$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module