A block of mass \( 2 M \) is attached to a massless spring with spring-constant \( k \). This bl...
0A 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 figure. The system is released from rest with the spring in its unstretched stale. 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] ,
(a) \( x_{0}=\frac{4 M g}{k} \)
(b) When spring achieves an extension of \( x_{0} / 2 \) for the first time, the speed of the block connected to the spring is \( 3 g \sqrt{\frac{M}{5 k}} \)
(c) \( a_{2}-a_{1}=a_{1}-a_{3} \)
(d) At an extension of \( x_{0} / 4 \) of the spring, the magnitude of acceleration of the block connected to the spring is \( \frac{3 g}{10} \)
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