Let the initial mass of man is m and cross-sectional area of his legs is A then mass is given as,
m=ρV=ρL3 and A=L2
[ assuming cubical shape of man having edge length L ]
External load acting on man is his weight (mg)
⇒stress=forcearea=mgA=ρL3gL2
⇒σi=ρLg ....(1)
When man's linear dimensions increases by a factor of 9, Let the final mass of man is m′ and area of leg is A′
⇒m′=ρV′=ρ(9L)3=93ρL3 and A′=(9L)2=92L2
⇒stress=forcearea=m′gA′=93ρL3g92L2
⇒σ′=9ρLg ....(2)
From Eq.(1) and (2),
⇒σ′σ=9
∴σ′=9σ
Hence stress in the leg will increase by a factor of 9.