Two blocks, of masses `M` and `2 M`, are connected to a light spring of spring constant `K` that has one end fixed, as shown in figure. The horizontal surface and the pulley are frictionless. The blocks are released from when the spring is non deformed. The string is light.
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Options

A. Maximum extension in the spring is `(4Mg)/(K)`.
B. Maximum kinetic energy of the system is `(2M^(2)g^(2))/(K)`.
C. Maximum energy stored in the spring is four times that of maximum kinetic energy of the system.
D. When kinetic energy of the system is maximum energy stored in the spring is `(4M^(2)g^(2))/(K)`.

Answer

A, B, C

Explanation

`(4 Mg)/(K)`
System will have maximum `KE` when net force on the system becomes zero. Therefore `2 Mg = T` and `T = kx rArr x = (2Mg)/(K)`
Hence `KE` will be maximum when `2M` mass has
gone down by `(2Mg)/(K)`.
Applying `W//E` theorem
`k_(f)-0 =2Mg.(2Mg)/(K)-(1)/(2)K.(4M^(2)g^(2))/(K^(2)) , k_(f) = (2M^(2)g^(2))/(K^(2))`
Maximum energy of spring
`(1)/(2) K.((4Mg)/(K))^(2) = (8 M^(2) g^(2))/(K)`
Therefore Maximum spring energy `= 4 xx "maximum" K.E`.
When `K.E` is maximum `x = (2Mg)/(K)`.
Spring enery ` = (1)/(2).K.(4M^(2)g^(2))/(K) = (2M^(2)g^(2))/(K)`.
i.e. `(D)` is wrong.