MCQ
A spring with spring constant $k $ is extended from $x = 0$to$x = {x_1}$. The work done will be
- A$kx_1^2$
- ✓$\frac{1}{2}kx_1^2$
- C$2kx_1^2$
- D$2k{x_1}$
✓
Answer
Correct option: B.
$\frac{1}{2}kx_1^2$
b
(b) $F=-k x$
(b) $F=-k x$
$d w=F \cdot d x$
$\int d x=\int_{0}^{x_1}-k x d x$
$w=-k \int_{0}^{x_1}xdx$
$=-k\left[\frac{x^{2}}{2}\right]_{0}^{x_{1}}$
$=-K\left[\frac{x_{1}^{2}}{2}\right]$
$w=-\frac{-k x_{1}^{2}}{2}$
$w=\frac{-1}{2} k x_{1}^{2}$
work done $=-(w)$
$=-\left[\frac{-1}{2} k x_{1}^{2}\right]$
$=\frac{1}{2} k x_{1}^{2}$
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