If an electron is subjected to aforce of `10^(-25)` N in an X-ray machine, then find out the time taken by the electron to cover a distance of 0.2 m. Take mass of the electron `10^(-30)` kg.

Options

A. `2xx10^(-6) s`
B. `2 xx 10^(-2) s`
C. `2 xx 10^(-3) s`
D. `2 xx 10^(3) s`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the given values
- Force (F) = \(10^{-25}\) N
- Mass of the electron (m) = \(10^{-30}\) kg
- Distance (s) = 0.2 m

### Step 2: Calculate the acceleration (a)
Using Newton's second law of motion, we know that:
\[ F = m \cdot a \]
We can rearrange this to find acceleration:
\[ a = \frac{F}{m} \]
Substituting the given values:
\[ a = \frac{10^{-25}}{10^{-30}} = 10^{5} \, \text{m/s}^2 \]

### Step 3: Use the equation of motion to find time (t)
We will use the equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Since the electron starts from rest, the initial velocity (u) is 0. Therefore, the equation simplifies to:
\[ s = \frac{1}{2} a t^2 \]
Substituting the known values:
\[ 0.2 = \frac{1}{2} \cdot 10^{5} \cdot t^2 \]
This simplifies to:
\[ 0.2 = 5 \times 10^{4} \cdot t^2 \]

### Step 4: Solve for \(t^2\)
Rearranging the equation gives:
\[ t^2 = \frac{0.2}{5 \times 10^{4}} = \frac{2 \times 10^{-1}}{5 \times 10^{4}} = \frac{2}{5} \times 10^{-5} \]
Calculating this gives:
\[ t^2 = 0.4 \times 10^{-5} \]

### Step 5: Take the square root to find \(t\)
Taking the square root:
\[ t = \sqrt{0.4 \times 10^{-5}} = \sqrt{4 \times 10^{-6}} = 2 \times 10^{-3} \, \text{s} \]

### Final Answer
The time taken by the electron to cover a distance of 0.2 m is:
\[ t = 2 \times 10^{-3} \, \text{s} \]

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