Question

A bullet of mass 2 g is having a charge of 2 µC. Through what potential difference must it be accelerated, starting from rest, to acquire a speed of 10 m/s?

• A. 50 kV
• B. 5V
• C. 50 V
• D. 5kV

Answer 1

The Correct Option is A

To solve this problem, we need to determine the potential difference required to accelerate a charged bullet from rest to a certain speed. Let's break down the problem step-by-step.

Given Data:

• Mass of the bullet, m = 2\,\text{g} = 2 \times 10^{-3}\,\text{kg}
• Charge of the bullet, q = 2\,\mu\text{C} = 2 \times 10^{-6}\,\text{C}
• Final speed of the bullet, v = 10\,\text{m/s}

Concept:

The kinetic energy acquired by the bullet when accelerated through a potential difference V is given by the equation:

K.E. = \frac{1}{2}mv^2

The work done by the electric field due to the potential difference is:

W = qV

By the conservation of energy, the work done on the bullet is equal to its kinetic energy:

qV = \frac{1}{2}mv^2

Solving for the Potential Difference:

Rearrange the equation to solve for V:

V = \frac{mv^2}{2q}

Substitute the given values into the equation:

V = \frac{(2 \times 10^{-3}\,\text{kg})(10\,\text{m/s})^2}{2 \times (2 \times 10^{-6}\,\text{C})}

V = \frac{(2 \times 10^{-3})(100)}{4 \times 10^{-6}}

V = \frac{0.2}{4 \times 10^{-6}}

V = 0.05 \times 10^6 = 50 \times 10^3 V

V = 50\,\text{kV}

Conclusion:

The bullet must be accelerated through a potential difference of 50 kV to acquire a speed of 10 m/s.

This matches the correct answer given: 50 kV.