a figure is mentioned(as i don't know how 2 scrap images in the question) like that.

1)draw a base line

2)a body B of mass 'm' on it

3) the upper end of B is attached to spring then with a string(rounded on a massless pulley)

4) the other part of the string is attached with a body A of mass M.

A is released from rest when the string is in its natural length. for the block B to leave contact with the ground at some stage. what should be the minimum mass of block A ??????????????

Dear Rajan,

you should analyze it that for minimum mass the block b will leave surface at maximum extension of spring, for masses greater, b will leave surface before maximum extension and for lesser masses it will not leave ever.

Let mass of block a  be M, we know at maximum extension velocity is 0 also extension in spring will be equal to desendent length  by block a

so by conservation of energy

    kx² /2 = Mgx

    kx = 2Mg

now fbd of a

  kx-Mg = Ma

  gives  a = g

fbd of b with normal force 0 for leaving surface

ma = kx

mg = 2Mg

M = m/2

which is amaging that we can use 5kg to lift 10 kg wieght by putting a spring in between, otherwise we need to have 10 kg wieght.

like my answer.

For just leaving the surface the normal by surfce will be 0 on block b

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