Question

# The value of $$x$$ in the formula $$Y=\dfrac { 2{ mgl }^{ x } }{ { 5bt }^{ 3 }e }$$ 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

Solution

## The correct option is A 3$$Y=\dfrac{2mgl^{x}}{5bt^{3}e}$$$$M^{1}L^{-1}T^{-2}=\dfrac{(M^{1})(LT^{-2})(L^{1})^{x}}{(L^{1})(L^{3})(L^{1})}$$$$\RightarrowL^{-1}=(L^{1})(L^{-5})(L^{1})^{x}$$$$\Rightarrow (-1) = 1 - 5 + x$$$$\Rightarrow x=3$$Physics

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