Pulleys and masses connected to a spring

JEE Advanced 2019 Paper 2, Question 2

A block of mass 2 M is attached to a massless spring with spring-constant k. This block is connected to two other blocks of masses M and 2 M using two massless pulleys and strings. The accelerations of the blocks are a_{1}, a_{2} and a_{3} as shown in the figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is x_{0}. Which of the following option(s) is/are correct?

[g is the acceleration due to gravity. Neglect friction]

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  1. x_{0}=\frac{4 M g}{k}
  2. When spring achieves an extension of \frac{x_{0}}{2} for the first time, the speed of the
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