Question

A stationary body of mass 5 g carries a charge of 5 $\mu$C. The potential difference with which it should be accelerated to acquire a speed of 10 m/s is:

• A. 4 kV
• B. 25 kV
• C. 50 kV
• D. 40 kV
• E. 2 kV

Hint:

The kinetic energy gained by a charged particle in an electric field is equal to the work done, which can be calculated using ${K.E.} = qV$.

Answer 1

The Correct Option is C

Step 1: The kinetic energy gained by the body when it is accelerated through a potential difference $V$ is given by: $$K.E = \frac{1}{2} m v^2 = qV$$ 
where: 
- $m = 5 \, {g} = 5 \times 10^{-3} \, {kg}$, 
- $v = 10 \, {m/s}$, 
- $q = 5 \, \mu C = 5 \times 10^{-6} \, {C}$. 
Step 2: The equation becomes: $$\frac{1}{2} \times 5 \times 10^{-3} \times (10)^2 = 5 \times 10^{-6} \times V$$ $$\Rightarrow 0.25 = 5 \times 10^{-6} \times V$$ 
Step 3: Solving for $V$: $$V = \frac{0.25}{5 \times 10^{-6}} = 50 \, {kV}$$ 
Thus, the required potential difference is 50 kV.