Question

From the fixed pulley, masses $2kg,1kg$ and $3kg$ are suspended as shown in the figure. Find the extension (in $m$) in the spring if spring constant $k=100N/m$ (Neglect oscillations due to spring)

Answer 1

Draw FBD for all the given blocks.

Find acceleration.

Applying NLM,
for $3kg$ mass, $3g-kx=3a\dots \left(i\right)$

for $1kg$ mass, $kx+g-T=a\dots \left(ii\right)$

for $2kg$ mass, $T-2g=2a\dots \left(iii\right)$

Adding $\left(i\right),\left(ii\right),\left(iii\right),$ we get
$a=\left(\frac{g}{3}\right)$

Find the extension in the spring.

Given, spring constant $k=100N/m$
Using equation $(i$)

$3g-kx=3\left(\frac{g}{3}\right)$

$x=\frac{2g}{k}=\frac{2\times 10}{100}$
Hence, $x=0.20m$

Final answer : $0.20$