A bullet of mass 40g moving with a speed of `90ms^(-1)` enters a heavy wooden block and is stopped after a direction of 60cm. The average resistive force exerted by the block on the bullet is

Options

A. 180N
B. 220N
C. 270N
D. 320N

Explanation

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

### Step 1: Convert the mass of the bullet to kilograms
The mass of the bullet is given as 40 grams. To convert this to kilograms:
\[ \text{Mass (m)} = 40 \text{ g} = \frac{40}{1000} \text{ kg} = 0.04 \text{ kg} \]

### Step 2: Convert the distance traveled into meters
The distance the bullet travels into the block is given as 60 cm. To convert this to meters:
\[ \text{Distance (s)} = 60 \text{ cm} = \frac{60}{100} \text{ m} = 0.6 \text{ m} \]

### Step 3: Identify the initial and final velocities
The initial velocity (u) of the bullet is given as:
\[ u = 90 \text{ m/s} \]
The final velocity (v) when the bullet stops is:
\[ v = 0 \text{ m/s} \]

### Step 4: Use the equation of motion to find acceleration
We will use the equation of motion:
\[ v^2 = u^2 + 2as \]
Rearranging this to solve for acceleration (a):
\[ a = \frac{v^2 - u^2}{2s} \]
Substituting the known values:
\[ a = \frac{0^2 - (90)^2}{2 \times 0.6} \]
\[ a = \frac{-8100}{1.2} = -6750 \text{ m/s}^2 \]

### Step 5: Calculate the average resistive force
Using Newton's second law, the average resistive force (F) exerted by the block on the bullet can be calculated using:
\[ F = m \cdot a \]
Substituting the values:
\[ F = 0.04 \text{ kg} \times (-6750 \text{ m/s}^2) \]
\[ F = -270 \text{ N} \]
The negative sign indicates that the force is in the opposite direction to the bullet's motion.

### Final Answer
The average resistive force exerted by the block on the bullet is:
\[ F = 270 \text{ N} \]

---