"A string of area of cross-section $4 \mathrm{~mm}^{2}$ and length $0.5 \mathrm{~m}$ is connected with a rigid body of mass $2 \mathrm{~kg}$. The body is rotated in a vertical circular path of radius $0.5 \mathrm{~m}$. The body acquires a speed of $5 \mathrm{~m} / \mathrm{s}$ at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _________ $\times 10^{-5}$. (use Young's modulus $10^{11} \mathrm{~N} / \mathrm{m}^{2}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)"

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$A = 4 \times {10^{ - 6}}$ m²

$l = 0.5$ m

$m = 2$ kg

${v_b} = 5$ m/s

${T_b} = mg + m\left( {{{V_b^2} \over l}} \right)$

$= 20 + 2 \times {{25} \over {{1 \over 2}}} = 120$ N

$${{\Delta l} \over l} = {{{T_b}} \over A} \times {1 \over Y} = {{120} \over {4 \times {{10}^{ - 6}}}} \times {10^{ - 11}} = 30 \times {10^{ - 5}}$$

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