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5.work,energy,power and collision — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics5.work,energy,power and collision1 Mark
MCQ
An elastic string of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is
  • A
    $\frac{1}{2} Ky ^2$
  • ✓
    $\frac{1}{2}Ky(2x+y)$
  • C
    $\frac{1}{2}K(x^2+y^2)$
  • D
    $\frac{1}{2} k(x+y)^2$
✓

Answer

Correct option: B.
$\frac{1}{2}Ky(2x+y)$
b
(b)

In the string elastic force is conservative in nature.

$\therefore W =-\Delta U$

Work done by elastic force of string,

$W =-\left( U _{ F }- U _{ i }\right)= U _{ i }- U _{ F }$

$W = \frac{1}{2} kx ^2-\frac{ k }{2}( x + y )^2$

$=\frac{1}{2} kx ^2-\frac{1}{2} k \left( x ^2+ y ^2+2 xy \right)$

$=\frac{1}{2} kx ^2-\frac{1}{2} ky ^2-\frac{1}{2} kx ^2-\frac{1}{2} k (2 xy )$

$=- kxy -\frac{1}{2} ky ^2$

Therefore, the work done against elastic force

$W _{\text {external }}=- W =\frac{ ky }{2}(2 x + y )$

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