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A rectangular beam which is supported at...

A rectangular beam which is supported at its two ends and loaded in the middle with weight `W` sags by an amount `delta` such that `delta=(Wl^(3))/(4Yd^(3)x),` where `l`, `d` and `Y` represent length, depth and elasticity respectively.
Guess the unknown factor using dimensional considerations :

A

breadth

B

`("breadth")^(2)`

C

`("breadth")^(3)`

D

mass.

Text Solution

Verified by Experts

The correct Answer is:
A
Hence `delta=(Wl^(3))/(4Yd^(3)x)`
`:. x=(Wl^(3))/(4Yd^(3)delta)`
`=([MLT^(-2)][L^(3)][L^(2)])/([MLT^(-2)][L^(3)][L])=[L].`
Hence `(a)` is the correct.
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