Question

The spring block system as shown in figure is in equilibrium. The spring connecting blocks $A$ and $B$ is cut. The mass of all the three blocks is $m$ and spring constant of both the spring is $k$. The amplitude of resulting oscillation of block $A$ is :

• A. $\frac{mg}{k}$
• B. $\frac{2mg}{k}$
• C. $\frac{3mg}{k}$
• D. $\frac{4mg}{k}$

Answer 1

The correct option is B $\frac{2mg}{k}$

Total force acting on block A before cutting spring=

Gravitation force of block A,B and C: $F_g=mg+mg+mg=3mg$

spring force $F_s=Kx$

and before cutting the spring $F_g=F_s$

$Kx=3mg$

$x=\frac{3mg}{K}$

where $x$ is the extension of spring just after cutting.

After cutting spring

when the block A in the mean position $Kx=mg$

mean position $x=\frac{mg}{K}$

Amplitude of oscillation of maximum strech-mean position

$A=\frac{3mg}{K}$$-\frac{mg}{K}$

$A=\frac{2mg}{K}$.

option B is correct.