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

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(A) \(9\)

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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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