Question

Two plates of same mass are attached rigidly to the two ends of a spring as shown in figure, One of the plates rests on a horizontal surface and the other results a compression y of the spring when it is in equilibrium state . The further minimum compression y of the spring when it is in equilibrium state. The further minimum compression required, so that when the force causing compression is removed the lover plate is lifted off the surface, will be:

• A. 0.5 y
• B. 3y
• C. 2y
• D. y

Answer 1

The correct option is C 2y

let the $2$ masses be $m$ and $m^{\prime }$

we can notice that due to the above mass $\left(mass\right)$ the spring is initially compressed to $y$ and the system is in equilibrium$,$

therefore we can say$,$ $ky=mg.$ $(K$ is spring constant assume$)$

$y=mg/k$------------------$\left(1\right)$

let the external force required to lift the system from the ground be $F.$

The additional compression done by $F$ be $X$

We can say that the downward force of the system is $2mg.$

We require a force of $KX$ such that $KX>2mg$

therefore$,$ $X>2mg/K$

$X>2y$ from equation $\left(1\right)$

Hence,'

option $\left(C\right)$ is correct answer.