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13.Oscillations
easy
The length of a spring is $l$ and its force constant is $k$. When a weight $W$ is suspended from it, its length increases by $x$. If the spring is cut into two equal parts and put in parallel and the same weight $W$ is suspended from them, then the extension will be
A
$2x$
B
$x$
C
$\frac{x}{2}$
D
$\frac{x}{4}$
Solution
(d) Spring is cut into two equal halves so spring constant of each part $= 2k$
These parts are in parallel so ${K_{eq}} = 2K + 2K = 4K$
Extension force (i.e. $W$) is same hence by using $F = kx$
==> $4k \times x' = kx$
==> $x' = \frac{x}{4}$.
Standard 11
Physics
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