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  • The length of an elastic string is a meter when the longitudinal tension is and b&nbsp

The length of an elastic string is a meter when the longitudinal tension is 4 \mathrm{~N} and b metre when the tension is 5 \mathrm{~N}. The length of the string (in metre) when the longitudinal tension is 9 \mathrm{~N} is

Option: 1

\mathrm{a-b}


Option: 2

\mathrm{5 b-4 a}


Option: 3

\mathrm{2 b-\frac{a}{2}}


Option: 4

\mathrm{4 a-3 b}


Answers (1)

best_answer

If L is the initial length, then the increase in length by a tension F is given by

                                          \mathrm{ l=\frac{F L}{\pi r^2 Y} }
Hence \mathrm{\quad a=L+l=L+\frac{4 L}{\pi r^2 Y}=L+4 c}                              (1)

and
                         \mathrm{ b=L+\frac{5 L}{\pi r^2 Y}=L+5 c }                                          (2)
where \mathrm{c=\frac{L}{\pi r^2 Y}}.

Solving (1) and (2) for L and c,

we get \mathrm{L=5 a-4 b \, \, and \, \, c=b-a.\, \, For \, \, F=9 \mathrm{~N}},

we have

                     \mathrm{ \begin{aligned} x & =L+\frac{9 L}{\pi r^2 Y} \\\\ & =L+9 c=(5 a-4 b)+9(b-a) \\\\ & =5 b-4 a \end{aligned} }

Posted by

Kuldeep Maurya

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