Question

For the given system, find the extension in the spring if $m_1=4\text{kg}$ and $m_2=6\text{kg}$. Take $g=10{\text{m/s}}^2$.

• A. $0.96\text{m}$
• B. $0.86\text{m}$
• C. $0.48\text{m}$
• D. $0.24\text{m}$

Answer 1

The correct option is A $0.96\text{m}$

From the FBD of blocks:


Applying Newton's $2^{\text{nd}}$ law of motion in direction of acceleration on blocks,
$T-m_{1}g=m_{1}a...\left(i\right)$
$m_{2}g-T=m_{2}a...\left(ii\right)$
Multiplying Eq. $\left(i\right)$ by $m_2$ and Eq. $\left(ii\right)$ by $m_1$ and subtracting,
$\Rightarrow (m_1+m_2)T=2m_1{m}_{2}g$
$T=\frac{2m_1{m}_{2}g}{m_1+m_2}$
$\therefore T=\frac{(2\times 4\times 6\times 10)}{4+6}=48\text{N}$


From F.B.D of pulley, since pulley is massless
$kx=2T$
$\Rightarrow x=\frac{2T}{k}=\frac{2\times 48}{100}$
$\therefore x=\frac{96}{100}=0.96\text{m}$