Question

A body acquires charge \( 8.0 \times 10^{-12} \, \text{C} \). The mass of the body:

• A. increases by \( 4.5 \times 10^{-7} \, \text{kg} \)
• B. decreases by \( 1.0 \times 10^{-6} \, \text{kg} \)
• C. decreases by \( 4.55 \times 10^{-23} \, \text{kg} \)
• D. increases by \( 9.1 \times 10^{-23} \, \text{kg} \)

Hint:

If a body gains electrons, its mass increases. If it loses electrons (positive charge), its mass decreases by the total mass of electrons lost.

Answer 1

The Correct Option is C

When a body acquires a positive charge, it means electrons are lost. Since electrons have mass, losing them causes the body's mass to decrease.
Each electron has: Charge, \( e = 1.6 \times 10^{-19} \, \text{C} \)
Mass, \( m_e = 9.1 \times 10^{-31} \, \text{kg} \)
Total charge acquired: \( Q = +8.0 \times 10^{-12} \, \text{C} \Rightarrow \) electrons lost
Number of electrons lost: \[ n = \frac{Q}{e} = \frac{8.0 \times 10^{-12}}{1.6 \times 10^{-19}} = 5 \times 10^7 \] Total mass lost: \[ \Delta m = n \times m_e = (5 \times 10^7) \times (9.1 \times 10^{-31}) = 4.55 \times 10^{-23} \, \text{kg} \] So, the mass of the body decreases by \( 4.55 \times 10^{-23} \, \text{kg} \).
Final answer: \({4.55 \times 10^{-23} \, \text{kg decrease}} \)