Spring Deformation problem

Question

In the diagram shown, there is no friction at any contact surface. Initially, the spring has no deformation and then a constant force F is applied as shown. What will be the maximum deformation in the spring? Consider all the strings to be sufficiently large. Consider the spring constant to be K.

Answer 1

correct option is B.

In the given system, the force acting on the block of mass 2M will have a force of 2F acting on it while the block M will have force F acting on it. On consideration of conditions in a state of maximum separation of the two blocks, the entire system comes to rest for a particular instant of time.

During this, the work done in the center of the mass frame will be zero. Therefore we get the total work done equation as W_spring+W_F+W_2F=0
. But, work done is a product of force and displacement for bodies and kinetic energy of springs.
Therefore,

According to the given data, the masses of the two bodies are M and 2M
.
Therefore we can write it as Mx₁=2Mx₂
Upon reduction we get,

Mx₁=2Mx₂

⇒x₁=2x₂

Substituting the value of x₁ in the displacement equation we get,

Substituting these values of x₁ and x₂ in the total energy equation of the system at rest we get,

Comments

How you wrote Mx1=2Mx2 ?

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Because masses of the two bodies are M and 2M