A string of area of cross – section 4 mm² and length 0.5 m is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5m. The body acquires a speed of 5 m/s at the bottom of the circular path. Strain produce in the string when the body is at bottom of the circle is________× 10^-5.

(use young’s modulus 10¹¹ N/m² and g = 10 m/s²)

<p>For circular motion:-</p><p><math><mrow><mi>T</mi><mo>−</mo><mi>m</mi><mi>g</mi><mo>=</mo><mfrac><mrow><mi>m</mi><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mi>r</mi></mrow></mfrac></mrow></math></p><p><math><mrow><mo>⇒</mo><mi>T</mi><mo>=</mo><mi>m</mi><mrow><mo> (</mo><mrow><mi>g</mi><mo>+</mo><mfrac><mrow><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><mi>r</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math></p><p><math><mrow><mo>=</mo><mn>2</mn><mrow><mo> (</mo><mrow><mn>1</mn><mn>0</mn><mo>+</mo><mfrac><mrow><mn>2</mn><mn>5</mn></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></mfrac></mrow><mo>)</mo></mrow><mo>=</mo><mn>1</mn><mn>2</mn><mn>0</mn><mi>N</mi></mrow></math></p><p><math><mrow><mo>⇒</mo><mi>S</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>i</mi><mi>n</mi><mo>=</mo><mfrac><mrow><mi>s</mi><mi>t</mi><mi>r</mi><mi>e</mi><mi>s</mi></mrow><mrow><mi>Y</mi></mrow></mfrac></mrow></math></p><p>= 30 × 10^-5</p>

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