Question

A man grows into a giant such that his height increases to 8 times his original height. Assuming that his density remains the same, the stress in the leg will change by a factor of

• A. \( 2 \sqrt{2} \)
• B. 4
• C. 16
• D. 8

Hint:

In problems related to stress and strain, remember that force is proportional to volume (for constant density), and stress is inversely proportional to are(A)

Answer 1

The Correct Option is B

The stress on the leg is related to the force applied and the area over which it is distribute(D) The force exerted by the man is proportional to his weight, which is proportional to his volume (since density remains constant). As the height of the man increases, his volume increases in proportion to the cube of the height (i.e., volume $\propto$ height\(^3\)). Since stress is defined as force per unit area, and area (cross-sectional area of the leg) increases with the square of the height (i.e., area $\propto$ height\(^2\)), we can find the factor by which stress changes: - Let the original height be \(h\). The new height is \(8h\). - The volume will increase by a factor of \(8^3 = 512\). - The area will increase by a factor of \(8^2 = 64\). Therefore, the stress, which is proportional to force per unit area, will increase by a factor of: \[ \text{Stress factor} = \frac{\text{Volume increase}}{\text{Area increase}} = \frac{512}{64} = 8 \] Thus, the stress will change by a factor of 4.