Question

The blocks are initially in equilibrium position then the minimum compression in the spring from its natural length so that the block of 2m leaves contact with the surface is $\frac{nmg}{k}$, where n equals to

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D 4

2m will leave the ground when spring is expanded by $x_2$ such that $k{x}_2=2mg$…..(1)

If it is initially compress by x1 from natural length

using conservation of energy

$WD=0$

$\Delta KE+PE=0$

$mg(x_1+x_2)+\frac{1}{2}k{x}_2^2-\frac{1}{2}k{x}_1^2=0$

put

$x_2=\frac{2m}{K}$

$inaboveeq,weget$

$mg+\frac{K}{2}(\frac{2mg}{k}-x_1)=0$

After solving $x_1=\frac{4mg}{k}$