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

JEE MainJEE Main 2022Mechanical Properties of Solids

Solution:

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$ =\frac{ mg +\frac{ mv ^2}{ R }}{ AY }$
$=\frac{20+\frac{2(5)^2}{0.5}}{3 \times 10^{-6} \times 10^{11}}=30 \times 10^{-5}$