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

Options

A. `9`
B. `(1)/(9)`
C. `81`
D. `(1)/(81)`

Answer

A

Explanation

`"Stress"= ("Force")/("area")`
The stress on the legs of the person can be calculated as :
Stress `=(mg)/(A)=("Volume(V)" xx "density"(pi)xxg)/("area(A)")`
Dimensionally, `V=L^(3), A= L^(2)`
Stress `=(L^(3)pg)/(L^2)`
Thus, stress `propto L`
As the linear dimensions of the person have increased by a factor of 9, thus the stress on the leg will also change by a factor of 9.