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Question

Two identical blocks A and B of mass 1 kg are joined together with a massless spring and are placed on a smooth surface as shown in the figure. If the block A moves with an acceleration of 3 m/s2, then the acceleration of the block B is:

A
4 m/s2
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B
1 m/s2
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C
3 m/s2
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D
2 m/s2
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Solution

The correct option is D 2 m/s2Considering the two blocks A and B as a system, 5 N force is the external force acting on the system. From the concept of centre of mass, we can find the acceleration of c.o.m by using the second law of motion, acom=Fmtotal where, mtotal is the total mass of the system. ⇒F=mtotal×acom⇒5=mtotal×acom ......(1) (Given) If mA is the mass of block A and mb is the mass of block B then acceleration acom, acom=mAaA+mBaBmA+mB ⇒mtotal×acom=mAaA+mBaB ⇒5=1×3+1×aB [From (1)] ⇒aB=2 m/s2 Alternate: Tension in the spring =1×3=3 N Applying Newton's law on body B, 5−3=1×a ⇒a=2 m/s2 Why this question?Concept -The concept of centre of mass converts a systemof many particles/bodies into a single particle/bodysystem. This makes our calculations easier.

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