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Two blocks A and B are connected by a massless string as represented in the diagram. A force of 30N is applied on block B, the distance travelled by centre of mass in 2s starting from the rest will be

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A.1mB.2mC.3mD.none of these

Answer
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Hint: First of all find the total mass of the centre of masses. Draw the free body diagram of the centre of mass of the system. Calculate the force acting on the centre of mass. Using this, find the acceleration of the centre of mass. Then use the second law of motion for calculating the displacement. This all will help you in solving this question.

Complete answer:
First of all, the mass of the block A is given as,
mA=10kg
Mass of the block B has been mentioned as,
mB=20kg
Time taken has been mentioned as,
t=2s
Force acting can be written as,
F=30N
Let us assume that the initial velocity on the body be,
u=0ms1
The total mass on the centre of mass will be,
M=mA+mB
Substituting the values in it,
M=10+20=30kg
The force acting on it will be equivalent to the force acting on the centre of mass. That is,
F=30N
The free body diagram of the centre of mass can be shown as,

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It is to be noted that the internal tension will not affect the centre of mass motion.
The acceleration of the centre of mass is mentioned as,
a=FM
Substituting the values in it,
a=3030=1ms2
According to the second equation of motion,
s=ut+12at2
Substitute the values in it will give,
s=12×1×22=2m

So, the correct answer is “Option B”.

Note:
The centre of mass is defined as the position described which is relative to an object or system of bodies. It will be the mean position of all the portions of the system which will be weighted in accordance with their masses. In short the centre of mass is a point where the whole mass of the system is assumed to be concentrated.
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