A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of ?

1 Answer
Sunayan S
Apr 8, 2018

By a factor #9#.

Explanation:

Let, the man as a rectangular cuboid.
My pc...
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Initially , I took the length #"l"#, breadth #"b"# and the height as #"h"# unit.

  • The pressure on the ground by the block is #=color(red)("voloume"xx"density"xxg#
  • The area of the block on the ground is #=color(red)("length"xx "breadth"#
  • #color(red)("stress"=("volume"xx"density"xxg)/("length"xx"breadth")="height"xx"denstity"xxg#
  • Stress is equivalent to pressure.
  • Initial #color(red)("stress"=h cdot rho cdot g#
  • Final #color(red)("stress"=9h cdot rho cdot g#

Stress changed by factor #(9h cdot rho cdot g)/(h cdot rho cdot g)=9#

Hope this helps...

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