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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
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B
2
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C
1
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D
4
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Solution

The correct option is A 3
$$Y=\dfrac{2mgl^{x}}{5bt^{3}e}$$

$$M^{1}L^{-1}T^{-2}=\dfrac{(M^{1})(LT^{-2})(L^{1})^{x}}{(L^{1})(L^{3})(L^{1})}
$$

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

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

$$ \Rightarrow x=3$$


Physics

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