Question

A block of mass 2M is attached to a massless spring with spring-constant k. This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are a₁, a₂ and a₃ 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]

(A) At an extension of  x₀/4 of the spring, the magnitude of acceleration of the block connected to the spring is 3g/10

(B)  x₀ = 4 Mg/k

(C)  a₂ -a₁ = a₁ -a₃

(D) When spring achieves an extension of  x₀/2 for the first time, the speed of the block connected to the spring is M 3g √M/5k

Answer 1

Correct option  (C)  a₂ -a₁ = a₁ -a₃

Explanation:

Using constraint relation

for the oscillation of mass '2m' (at mean position)