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When a load of 80N is suspended from a string, its length is 101mm. If a load of 100N is suspended, its length is 102mm. If a load of 160N is suspended from it, then length of the string is ....... cm (Assume the area of cross- section unchanged)

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15.5

13.5

16.5

10.5

answer is D.

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Detailed Solution

Given,

$T_{1} = 80 N, L_{1} = 101 mm, T_{2} = 100 N, L_{2} = 102 mm, T_{3} = 160 N$

We know that natural length is,

$L = \frac{L_{1} T_{2} - L_{2} T_{1}}{T_{2} - T_{1}} = \frac{101 \times 100 - 102 \times 80}{100 - 80} = \frac{10100 - 8160}{20} = 97 cm$

$\frac{T_{1}}{T_{3}} = \frac{4}{l - 97}$

$l_{3} - 97 = 8 \Rightarrow l_{3} = 105 mm = 10.5 cm$

Hence the correct answer is 10.5cm.

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