Question 179: Properties of Matter

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 :

Accepted Answer

To determine how the stress in the leg changes when a man's linear dimensions increase by a factor of 9, we can analyze the relationship between the dimensions and the stress on the legs.
First, let's establish some relationships:
Linear dimensions (length, width, height) increase by a factor of 9.
Density remains the same.
Stress is defined as force per unit area:
$$ 	ext{Stress} = \dfrac{	ext{Force}}{	ext{Area}} $$
Since density remains constant, the volume and thus the mass of the man will change according to the cube of the linear dimensions. Since the linear dimension changes by a factor of 9, the volume (and hence the mass) changes by a factor of:
$$ 9^3 = 729 $$
Therefore, the weight (force due to gravity) also increases by a factor of 729.
The cross-sectional area of the leg is proportional to the square of the linear dimensions. Thus, if the linear dimension increases by a factor of 9, the cross-sectional area increases by a factor of:
$$ 9^2 = 81 $$
Now, substituting these factors into the stress formula:
$$ 	ext{New Stress} = \dfrac{	ext{New Force}}{	ext{New Area}} = \dfrac{729 	imes 	ext{Original Force}}{81 	imes 	ext{Original Area}} $$
Simplifying, we get:
$$ 	ext{New Stress} = 9 	imes \dfrac{	ext{Original Force}}{	ext{Original Area}} = 9 	imes 	ext{Original Stress} $$
Thus, the stress in the leg increases by a factor of 9. Therefore, the correct answer is:
Option B: 9

Answer

$${1 \over {81}}$$

Answer

9

Answer

$${1 \over {9}}$$

Answer

81

Properties of Matter

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 :

Choose the correct answer: