A bullet of mass 5g is fired from a gun at a speed of 100m/s. If the barrel of the gun is of length 1m, then what will be the force caused by the gas, on the bullet?

Options

A. 20N
B. 25N
C. 30N
D. 35N

Explanation

To solve the problem, we will use the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

### Step-by-Step Solution:

**Step 1: Convert the mass of the bullet from grams to kilograms.**
- Given mass of the bullet = 5 g
- To convert grams to kilograms, we use the conversion factor \(1 g = 0.001 kg\).
- Therefore, \(m = 5 g = 5 \times 10^{-3} kg\).

**Step 2: Calculate the kinetic energy (KE) of the bullet.**
- The formula for kinetic energy is given by:
\[ KE = \frac{1}{2} m v^2 \]
- Where:
- \(m\) = mass of the bullet = \(5 \times 10^{-3} kg\)
- \(v\) = speed of the bullet = \(100 m/s\)
- Plugging in the values:
\[ KE = \frac{1}{2} \times (5 \times 10^{-3}) \times (100)^2 \]
\[ KE = \frac{1}{2} \times (5 \times 10^{-3}) \times 10000 \]
\[ KE = \frac{1}{2} \times 50 = 25 J \]

**Step 3: Use the work-energy theorem to relate work done to force.**
- According to the work-energy theorem:
\[ Work = Force \times Displacement \]
- Here, the displacement \(S\) is the length of the barrel of the gun, which is given as \(1 m\).
- Therefore, we can write:
\[ Work = F \times S \]
- Rearranging for force \(F\):
\[ F = \frac{Work}{S} \]

**Step 4: Substitute the values to find the force.**
- We know that the work done is equal to the kinetic energy calculated:
\[ F = \frac{KE}{S} = \frac{25 J}{1 m} = 25 N \]

### Final Answer:
The force caused by the gas on the bullet is **25 N**.