A block of mass \( 2 \mathrm{M} \) is attached to a massless spring...
0A block of mass \( 2 \mathrm{M} \) is attached to a massless spring with spring-constant \( \mathrm{k} \). This block is connected to two other
\( \mathrm{P} \) blocks of masses \( \mathrm{M} \) and \( 2 \mathrm{M} \) using two massless pulleys and strings. The accelerations of the blocks are \( a_{1}, a_{2} \) and
W \( \mathrm{a}_{3} \) as shown in figure. The system is released from rest with the spring in its unstretched state. The maximum extension of the spring is \( \mathrm{x}_{0} \). Which of the following option(s) is/are correct? [JEE Advanced-2019] [ \( \mathrm{g} \) is the acceleration due to gravity. Neglect friction]
(a) \( \mathrm{x}_{0}=\frac{4 \mathrm{Mg}}{\mathrm{k}} \)
(b) When spring achieves an extension of \( \frac{x_{0}}{2} \) for the first time, the speed of the block connected to the spring is \( 3 g \sqrt{\frac{M}{5 \mathrm{k}}} \)
(c) \( \mathrm{a}_{2}-\mathrm{a}_{1}=\mathrm{a}_{1}-\mathrm{a}_{3} \)
(d) At an extension of \( \frac{x_{0}}{4} \) of the spring, the magnitude of acceleration of the block connected to the spring is \( \frac{3 \mathrm{~g}}{10} \)
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