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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Mechanical Properties of Solids

NTA Abhyas 2020 · Physics · Mechanical Properties of Solids

When a metallic wire is held under a tensile force F _ 1 , the...

When a metallic wire is held under a tensile force F1{F}_{1}, the length of the wire is L1{L}_{1}. If the force is changed to F2{F}_{2} , the length of the wire is L2.{L}_{2}. The original length LL& of the wire is

Options

  1. AL1F1+L2F2F1+F2\dfrac{{L}_{1}{F}_{1} + {L}_{2}{F}_{2}}{{F}_{1} + {F}_{2}}
  2. BL2−L1F1+F2\dfrac{{L}_{2} - {L}_{1}}{{F}_{1} + {F}_{2}}
  3. CF1L2−F2L1F1−F2\dfrac{{F}_{1}{L}_{2} - {F}_{2}{L}_{1}}{{F}_{1} - {F}_{2}}
  4. DF1L1−F2L2F1−F2\dfrac{{F}_{1}{L}_{1} - {F}_{2}{L}_{2}}{{F}_{1} - {F}_{2}}

Correct answer

C. F1L2−F2L1F1−F2\dfrac{{F}_{1}{L}_{2} - {F}_{2}{L}_{1}}{{F}_{1} - {F}_{2}}

Step-by-step solution

F ∝ dl<br/><br/><br /><br />{F}_{1} ∝ \left({L}_{1} - l\right) ⇒ ( 1 )<br/><br/><br /><br />{F}_{2} ∝ \left({L}_{2} - l\right) ⇒ ( 2 )<br/><br/><br /><br />\dfrac{F1}{F2} = \dfrac{{L}_{1} - l}{{L}_{2} - l}<br/><br/><br /><br />{F}_{1}{L}_{2} - {F}_{1}l = {F}_{2}{L}_{1} - {F}_{2}l<br/><br/>(F1−F2)l=F1L2−F2L1<br /><br />\left({F}_{1} - {F}_{2}\right)l = {F}_{1}{L}_{2} - {F}_{2}{L}_{1}

l=F1L2−F2L1F1−F2l = \dfrac{{F}_{1}{L}_{2} - {F}_{2}{L}_{1}}{{F}_{1} - {F}_{2}}
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