A block of mass m is connected to another block of mass M by a massless spring constant K. Blocks are kept on a smooth horizontal plane. Initially both the blocks are at rest and spring is unstressed. Force F is applied on M to right as shown in the figure then which of the following is correct----

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Acceleration of the centre of mass is $\frac{F}{M + m}$

At the instant of maximum elongation of the spring, acceleration of centre of mass is zero.

At maximum extension of the spring acceleration of centre of mass is $\frac{F}{M + m}$

At maximum extension, velocity of both the blocks will be same.

answer is A, C, D.

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Detailed Solution

Irrespective of what is the extension or compression in the spring, as net external force is F, acceleration of centre of mass is $\frac{F}{M + m}$ .
At maximum extension, relative velocity between the blocks is zero or velocity of both the blocks is same.
Net external force= F at maximum extension

$\Rightarrow a = \frac{F}{M + m}$

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