    Question

# The system shown is in equilibrium. Find the accelerations of the blocks A, B and C just after the spring between B and C is cut. All blocks are of equal masses ‘m′ each and springs are of equal stiffness. (Assume springs to be ideal and take downward acceleration to be positive). A
+g,+g,g
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B
g2,g2,+g
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C
+g,g2,g
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D
0,g2,g
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Solution

## The correct option is B −g2,−g2,+gSince A and B are connected by inextensible string, therefore both will experience same acceleration. Hence they will be considered as single system. Let the extension in the string between ceiling and block A be x1 and that for spring between B and C be x2 Before cutting For block C, Kx2=mg For block A and B, Kx1=kx2+2mg Since Kx2=mg ⇒Kx1=3mg After Cutting, spring force kx2=0 Let a be the acceleration of block A and B. For block A and B, Kx1−2mg=2ma Since Kx1=3mg ⇒3mg−2mg=2ma a=g2 (Upwards) ⇒aB=aC=−g2 Let the acceleration for block C be ac, then from the free body diagram, mg=mac ac=g (Downwards)  Suggest Corrections  0      Explore more