Four blocks of masses 1 kg, 2kg, 4 kg, and 8kg are connected with three ideal springs. The whole system is released from rest on a frictionless horizontal surface. After some time the acceleration of

Question

Four blocks of masses 1 kg, 2kg, 4 kg, and 8kg are connected with three ideal springs. The whole system is released from rest on a frictionless horizontal surface. After some time the acceleration of 1 kg and 4 kg are found to be zero while the middle spring is found to be compressed by 0.1 m. At the same instant of time the ratio of acceleration of 2 kg and 8 kg block is :

$1 kg, 2 kg, 4 kg, 8 kg$

TestHub · Accepted Answer

Accelerations of the 1 kg and 4 kg blocks are zero, so the outer springs exert no force at this instant

The middle spring pushes the 2 kg and 8 kg blocks with $k x = 200 \times 0.1 = 20$ N each

$a_{2} = \frac{20}{2} = 10$ m/s $^{2}$ , $a_{8} = \frac{20}{8} = 2.5$ m/s $^{2}$

$\frac{a _{2}}{a _{8}} = 4$

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