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Mechanical equilibrium force cases
Question

Two blocks of masses M and m are connected to each other by a massless string and spring of force constant k as shown in the figure. The spring passes over a frictionless pulley connected rigidly to the edge of a stationary block A. The coefficient of friction between block M and the plane horizontal surface of A is μ. The block M slides over the horizontal top surface of A and block m slides vertically downwards with the same speed. The mass M is equal to

Moderate
Solution

When the system of two blocks of masses M and m is either at rest or moving with the same speed, no net force acts on them.

In this equilibrium state,

T=μR=μMg and T=mg

  μMg=mgM=mμ

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