Question

Which of the following statements are true?
A) Charge cannot exist without mass but mass can exist without charge
B) Charge is invariant but mass varies with velocity
C) Charge is conserved but mass alone may not be conserved

Answer 1

Hint: In this question, we will discuss the basics of a charged body, velocity and mass of a body. Further, these will help us get the answer to our question. Also, we will study the basics of conservation of mass, when two bodies collide, for our better understanding.

Complete answer:
A) As we know that a charged body has electrons which have mass whereas a body can be neutral i.e., can have no charge. So, this statement is correct.
B) Here, mass is a variant. As we know, according to Einstein’s equation, when a body is travelling with a speed comparable to that of light, its mass change is given as:
${m_f} = \dfrac{{{m_i}}}{{\sqrt {1 - \dfrac{{{v^2}}}{{{c^2}}}} }}$B)
So, this statement is also correct.
C) At last, we know that a charge is invariant. Charge is independent of velocity, but as we know that the mass of a particle will exponentially rise as the velocity approaches the velocity of light.
Therefore, we can conclude that all the three statements are true.

Additional information:
From the law of conservation of mass which says that mass can neither be created nor destroyed in any chemical reactions. Also, it can be defined as the mass of any one element at the beginning of a reaction will equal the mass of that element at the end of the reaction.
We know that collision means when two objects come in contact with each other for a very short period. Collision is an interaction between two masses for a very short interval where the momentum and energy of the colliding masses changes. Here are two types of collision: first id elastic collision where the energy remains same after interaction or collision and second is inelastic collision where the final energy changes after the collision of the particles or body.

Note:
The resulting mass, energy or velocity after the collision of two particles depends on its direction and magnitude as well. During the solution, one should see that laws of conservation are not violated, i.e., mass can neither be created nor be destroyed and similarly for energy of the particles as well.