Question

In the figure given below, block $A$ is of mass $m$ and block B is of mass $2m$. The spring has force constant $k$. All the surfaces are smooth and the system is released from rest with the spring unstretched. Maximum extension in the spring is

• A. $\frac{mg}{2k}$
• B. $\frac{4mg}{k}$
• C. $\frac{2mg}{k}$
• D. $\frac{mg}{4k}$

Answer 1

The correct option is B $\frac{4mg}{k}$

At maximum extension $\left(x_m\right)$ in the spring :
$v_A=v_B=0$
Applying conservation of mechanical energy :
Decrease in gravitaitonal potential energy of block B = Increase in elastic ptotential energy of spring.
$\Rightarrow m_{B}g{x}_m=\frac{1}{2}K{x}_m^2$
(displacement of block B will be equal to the extension in spring)
or $2mg{x}_m=\frac{1}{2}K{x}_m^2$
$\therefore x_m=\frac{4mg}{K}$