Basic Maths and Units and DimensionsHard

Question

Block ′A′ is hanging from a vertical spring and is at rest. Block ′B′ strikes the block ′A′ with velocity ′v′ and sticks to it. Then the value of ′v′ for which the spring just attains natural length is:
             

Options

A.
B.
C.
D.none of these

Solution

           
The initial extension in spring is x0 =
Just after collision of B with A the speed of combined mass is  .
For the spring to just attain natural length the combined mass must rise up by x0 =  (sec fig.) and comes to rest.
Applying conservation of energy between initial and final states

Solving we get v = 

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