If speed (V), acceleration (A) and force (F) | vedclass

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

Question

$\begin{array}{l}
\frac{F}{A} = y \cdot \frac{{\Delta \ell }}{\ell }\,\,;\,\,\left[ Y ight] = \frac{F}{A}\
Now\,from\,\dim ension\
\,\,\,\,\,\,

Vedclass · Accepted Answer

${V^{ - 4}}{A^{2}}F$

Vedclass · Answer

$\begin{array}{l}
\frac{F}{A} = y \cdot \frac{{\Delta \ell }}{\ell }\,\,;\,\,\left[ Y ight] = \frac{F}{A}\
Now\,from\,\dim ension\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,F = \frac{{ML}}{{{T^2}}}\,\,;\,\,L = \frac{F}{M} \cdot {T^2}\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{L^2} = \frac{{{F^2}}}{{{M^2}}}{\left( {\frac{V}{A}} ight)^4}\,\,\,\,\,\,T = \frac{V}{A}\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{L^2} = \frac{{{F^2}}}{{{M^2}{A^2}}}\frac{{{V^4}}}{{{A^2}}}\,\,\,\,\,\,F = MA\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,{L^2} = \frac{{{V^4}}}{{{A^2}}}\
\left[ Y ight] = \frac{{\left[ F ight]}}{{\left[ A ight]}} = {F^1}{V^{ - 4}}{A^2}
\end{array}$

If speed $(V)$, acceleration $(A)$ and force $(F)$ are considered as fundamental units, the dimension of Young’s modulus will be

Similar Questions

In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.

Which of the following quantities has a unit but dimensionless?

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)

$(A)$ $M \propto \sqrt{ c }$ $(B)$ $M \propto \sqrt{ G }$ $(C)$ $L \propto \sqrt{ h }$ $(D)$ $L \propto \sqrt{G}$

If the capacitance of a nanocapacitor is measured in terms of a unit $u$ made by combining the electric charge $e,$ Bohr radius $a_0,$ Planck's constant $h$ and speed of light $c$ then

If force $({F})$, length $({L})$ and time $({T})$ are taken as the fundamental quantities. Then what will be the dimension of density