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