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

A body gaining a positive charge indicates the loss of electrons. As electrons possess mass, their removal results in a reduction of the body's mass.

Individual electron properties:
Charge, \( e = 1.6 \times 10^{-19} \, \text{C} \)
Mass, \( m_e = 9.1 \times 10^{-31} \, \text{kg} \)

Net charge acquired:
\( Q = +8.0 \times 10^{-12} \, \text{C} \Rightarrow \) electrons were lost.

Quantity of electrons lost:
\[n = \frac{Q}{e} = \frac{8.0 \times 10^{-12}}{1.6 \times 10^{-19}} = 5 \times 10^7\]Total mass loss:
\[\Delta m = n \times m_e = (5 \times 10^7) \times (9.1 \times 10^{-31}) = 4.55 \times 10^{-23} \, \text{kg}\]Consequently, the body's mass diminishes by \( 4.55 \times 10^{-23} \, \text{kg} \).

Final answer: \({4.55 \times 10^{-23} \, \text{kg decrease}} \)