Force (F) and density (d) are related as F = | vedclass

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

Question

(A) According to the principle of homogeneity of dimensions,quantities added together must have the same dimensions.Since $\beta$ is added to $\sqrt{d

Vedclass · Accepted Answer

$[M^{3/2} L^{-1/2} T^{-2}]$

Vedclass · Answer

(A) According to the principle of homogeneity of dimensions,quantities added together must have the same dimensions.Since $\beta$ is added to $\sqrt{d}$,the dimensions of $\beta$ must be equal to the dimensions of $\sqrt{d}$.Density $d = [M L^{-3}]$,so $\sqrt{d} = [M^{1/2} L^{-3/2}]$.Thus,$[\beta] = [M^{1/2} L^{-3/2}]$.The denominator $(\beta + \sqrt{d})$ will also have the same dimensions: $[\beta + \sqrt{d}] = [M^{1/2} L^{-3/2}]$.The given equation is $F = \frac{\alpha}{\beta + \sqrt{d}}$.Rearranging for $\alpha$,we get $\alpha = F 	imes (\beta + \sqrt{d})$.Force $F = [M L T^{-2}]$.Substituting the dimensions: $[\alpha] = [M L T^{-2}] 	imes [M^{1/2} L^{-3/2}]$.$[\alpha] = [M^{1 + 1/2} L^{1 - 3/2} T^{-2}] = [M^{3/2} L^{-1/2} T^{-2}]$.

Force $(F)$ and density $(d)$ are related as $F = \frac{\alpha}{\beta + \sqrt{d}}$. The dimensions of $\alpha$ are:

Similar Questions

Given that $v$ is speed,$r$ is the radius,and $g$ is the acceleration due to gravity. Which of the following is dimensionless?

Find the dimensional formula of $\frac{a}{b}$ in the equation $F=a \sqrt{x}+b t^2$,where $F$ is force,$x$ is distance,and $t$ is time.

Which of the following statements is incorrect?

Heat produced in a current-carrying conducting wire depends on current $I$,resistance $R$ of the wire,and time $t$ for which the current is passed. Using these facts,obtain the formula for heat energy.

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