two blocks of masses m1 and m2 are connected by a spring in a frictionless plane. when a force F is applied on the mass m2 then what will be the maximum extension in the spring? plz include the explanation

Dear student,
We have the two masses, m₁ and m₂. The applied force is F, k is the spring constant, X is the extension of the spring.

Then, the total mass of the system is (assuming spring to be massless):
M = m₁ + m₂

Now using Newton's second law, we can find the acceleration of the system as:
a = F / (m₁ + m₂)

Hence the tension in the spring would be given by:
T = m₁×a
T = m₁×F/(m₁ + m₂)

Therefore, by Hooke’s law, we can find the extension of the spring.
F = k×X
Since F = T, so
m₁ × F/(m₁ + m₂) = k×X
So, X = m₁×F / [k×(m₁ + m₂)]
Regards