A string of length '/' and radius 'a' is stretched between two fixed points A and B without tension. The middle point of the string is pulled to a small distance 'd' in a direction,perpendicular to the original length of the string. If the Young's modulus of the material of the string is Y, the energy stored in the string is:

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πa2Yd2/l

πa2Yd

2πYa2d4/l3

Ya2l2/d

answer is C.

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Detailed Solution

∆l=2d2+l24-l=2l24+d212-l =2121+4d2l212-l=2d2l =l1+124d2l2-l=2d2l Strain =∆ll=2d2l2 Energy stored =12Y(strain)2∆V=12Y2d2l22πa2l =2πa2Yd4l3

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