Question

Find the elongation in the spring for the system shown in the figure. ($g=10m/s^2$)

• A. $25\text{cm}$
• B. $50\text{cm}$
• C. $75\text{cm}$
• D. $100\text{cm}$

Answer 1

The correct option is A $25\text{cm}$

The given spring problem can be converted easly to string problem as shown
Here, the spring force $kx$ will be equal to the tension $T$ in the string

So, we can find the acceleration of the system as
$\text{a}=\frac{\text{supporting Force- opposing force}}{\text{Total mass}}$
$=\frac{5g-3g}{8}=\frac{g}{4}{\text{m/s}}^2$

Hence from the FBD of $5\text{kg mass}$ we have $5g-T=5a⟹T=5(g-a)=5\left(\frac{3g}{4}\right)N$
$\therefore T=kx⟹kx=\frac{15\text{g}}{4}\Rightarrow x=\frac{150}{4\times 150}=0.25\text{m}=25cm$.