Five balls, numbered 1 to 5, are suspended using separate threads. Pairs (1, 2), (2, 4), (4, 1) show electrostatic attraction, while pairs (2, 3) and (4, 5) show repulsion, therefore ball 1 must be:
A. Positively charged
B. Negatively charged
C. Neutral
D. Made of metal

Hint: In order to solve the above question we need to understand the concept of coulomb’s law of force of attraction and repulsion. Also we should know the sum of forces acting on the system.

Complete step by step answer:
Since the first ball does not come under the list of repulsion such that it’s possible that it does not contain any charge. As per the above data the first ball is being attracted by the second and fourth ball. So it must be second and fourth both contain similar charges, but here it is also given that second and fourth balls attract each other. Hence the second and fourth balls are taken as oppositely charged.

Since the second, third and fourth, first balls are repelling each other and fourth and fifth balls are attracting each other which means second, third and first balls are similarly charged each other but fourth is not attracted to fifth ball. Third and fourth balls attract each other which proves that second and first balls are similarly charged as fifth balls. Hence this shows that the fifth ball is negatively charged.

Let us consider the first ball has a negative or positive type of charge. The first and second balls must have different charges. The second and fourth balls must have different charges which means the first and fourth balls must have similar charges but force of attraction is also there in first and fourth which is not possible.

There must be a neutral because second and fourth balls show attraction means have opposite then first and fourth balls should have the same charge but as they also show property of attraction. First ball should be electricity neutral. Another side it can be seen that the second ball is positively charged then the fourth ball is negatively charged because the second and fourth showing attraction property. Now the second and third balls also show repulsion because of positive charges. Similarly because fourth and fifth balls show repulsion because of negative charges and we remain with the first ball and neither positively nor negatively charge. Hence this indicates the first ball has no charge so it should be neutral.

So, the correct answer is “Option B”.

Note:
According to Coulomb's electrostatic theory, similar or like charges repel each other and unlike charges attract each other. This means charges of the same sign will move away or push each other with repulsive forces while charges with opposite signs will try to pull each other with the attractive force.