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Question

Two blocks of mass 1 kg and 2 kg are connected by a vertical spring of spring constant k=2000 N/m such that the 2 kg block is resting on the floor (assume frictionless). The upper block of mass 2 kg is pushed down by a distance x and released, and it executes SHM. What is the maximum value of x so that the 2 kg block does not leave the floor?

A
5 mm
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B
10 mm
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C
15 mm
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D
none of the above
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Solution

The correct option is B 10 mm

If x0 is the compreesion in the spring at equilibrium position, then

kx0=mg
x0=1×102000=12

Now extension at the top most position in spring will be
x=(x12) cm

So as we can understand from the diagram, block of mass 2 kg will leave the floor when N=0.
So,
kx=mg
2000×x12100=2×10
x=1.5 cm=15 mm

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