MCQ
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
- ✓$9$
- B$\frac{1}{9}$
- C$81$
- D$\frac{1}{{81}}$
✓
Answer
Correct option: A.
$9$
a
As liner dimension increases by a factor of $9$
As liner dimension increases by a factor of $9$
$\frac{{{v_f}}}{{{v_i}}} = {9^3}$
Density remains same
So, mass $\propto$ Volume
$\frac{{{m_f}}}{{{m_i}}} = {9^3}\,\,\, \Rightarrow \,\,\,\frac{{{{\left( {Aera} \right)}_f}}}{{{{\left( {Aera} \right)}_i}}} = {9^2}$
$Stress\left( \sigma \right) = \frac{{force}}{{area}} = \frac{{\left( {mass} \right) \times g}}{{area}}$
$\frac{{{\sigma _2}}}{{{\sigma _1}}} = \left( {\frac{{{m_f}}}{{{m_i}}}} \right)\left( {\frac{{{A_i}}}{{{A_f}}}} \right) = \frac{{{9^3}}}{{{9^2}}} = 9$
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