Question # 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 : ( quad )

# 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 : ( quad )

(1) 81

(2) ( frac{1}{81} )

(3) 9

(4) ( frac{1}{9} )

Solution

( begin{array}{l}begin{aligned} text { Stress } &=frac{text {Force}}{text {area}} &=frac{m g}{A} &=frac{text {Volume} times text {density} times g}{text {Area}} end{aligned} text { Stress } & =frac{L^{3} p g}{L^{2}} text {stress} & infty Lend{array} )

Change in stress is proportional to change in length Therefore, stress

changes by a factor of ( 9 . ) (a) option is

correct