JEE Main Solved Paper 2017 Question 18
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 : [JEE Main Solved Paper-2017]
Options:
A) 81
B) $ \frac{1}{81} $
C) 9
D) $ \frac{1}{9} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ Stress=\frac{Force}{area}$ Let linear dimensions be l,b,h.
$ Stress=\frac{Force}{l\times b}$
Now, dimensions increase by factor of g.
So, Now $ S′=\frac{Force}{9l\times 9b}= \frac{ma}{81lb}$
$S′=\frac{\rho Va}{81lb}$
∴ $S′=\frac{9^3 V}{81lb}\times \frac{lb}{V}$
S′=9S Hence stress in leg will change by factor of 9
