A rectangular beam which is supported at its two ends and leaded in the middle with weight w sags by an amount such that δ=wl34Yd3, where ℓ,d and y represent length, depth and elasticity respectively. Guess the unknown factor using dimensional considerations

[Sl3][4yd3δ]=[MLT−2][L3][L2][MLT−2][L3][L]=[L]

[Sl3][4yd3δ]=[MLT−2][L3][L2][MLT−2][L3][L]=[L]

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A rectangular beam which is supported at its two ends and leaded in the middle with weight w sags by an amount such that $δ = \frac{w l^{3}}{4 Y d^{3}},$ where $ℓ, d$ and y represent length, depth and elasticity respectively.
Guess the unknown factor using dimensional considerations

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${(breadth)}^{3}$

${(breadth)}^{2}$

Mass

Breadth

answer is A.

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$\frac{[S l^{3}]}{[4 y d^{3} δ]} = \frac{[{MLT}^{- 2}] [L^{3}] [L^{2}]}{[{MLT}^{- 2}] [L^{3}] [L]} = [L]$

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