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Question

Two blocks A and B of same mass m connected by a light spring are suspended by an inextensible string as shown in the figure. Find the magnitude of the acceleration of block A and B just after the string is cut.

A
2g,0
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B
0,2g
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C
g,g
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D
2g,2g
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Solution

The correct option is A 2g,0
When block A and B are in equilibrium position, let To be the spring force and T be the tension in the string.
F.B.D of B

To=mg(1)
F.B.D of A

T=mg+T0
T=2 mg(2)
When string is cut, tension T becomes zero. but spring does not change its shape just after cutting . So spring force acts on mass B.
F.B.D of 'B'

Tomg=maB
Since To=mg [Using (1)]
aB=0

F.B.D of 'A'

mg+To=m.aA
2mg=m.aA
aA=2g(downwards)

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