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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).

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Solution

The correct option is **B** −g2,−g2,+g

Since 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)

Since 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)

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