Question

The value of $x$ in the formula $Y=\frac{2{mgl}^x}{{5bt}^{3}e}$ is (Where $m$ is the mass, $g$ is acceleration due to gravity, $l$ is the length, $b$ is the breadth, $t$ is the thickness, $e$ is the extension and $Y$ is Young's Modulus.)

• A. 3
• B. 2
• C. 1
• D. 4

Answer 1

The correct option is A 3

$Y=\frac{2mg{l}^x}{5b{t}^{3}e}$

$M^1{L}^{-1}{T}^{-2}=\frac{\left(M^1\right)\left(L{T}^{-2}\right)(L^1{)}^x}{\left(L^1\right)\left(L^3\right)\left(L^1\right)}$

$\Rightarrow L^{-1}=\left(L^1\right)\left(L^{-5}\right)(L^1{)}^x$

$\Rightarrow (-1)=1-5+x$

$\Rightarrow x=3$