**Bullet Mass and Velocity**

The given problem states that a bullet with a mass of 10 grams is moving with a velocity of 150 m/s. This information is crucial in determining the force exerted by the bullet on the wooden block.

**Calculating the Initial Kinetic Energy**

To begin solving this problem, we need to calculate the initial kinetic energy of the bullet. The formula for kinetic energy is:

Kinetic Energy = 0.5 * mass * velocity^2

Using this formula, we can substitute the given values:

Kinetic Energy = 0.5 * 0.01 kg * (150 m/s)^2

Simplifying the equation, we find that the initial kinetic energy of the bullet is:

Kinetic Energy = 0.5 * 0.01 kg * 22500 m^2/s^2 = 112.5 Joules

**Penetration Depth**

It is stated that the bullet penetrates the wooden block up to a depth of 6 cm. This information allows us to calculate the average force exerted by the bullet on the block.

**Determining the Work Done**

The work done by the bullet in penetrating the block can be calculated using the formula:

Work Done = Force * Distance

In this case, the distance is given as 6 cm, which is equivalent to 0.06 meters. We need to calculate the force exerted by the bullet, so we rearrange the formula:

Force = Work Done / Distance

**Calculating the Average Force**

Substituting the known values into the formula:

Force = 112.5 J / 0.06 m = 1875 N

Hence, the average force exerted by the bullet on the wooden block is 1875 Newtons.

**Explanation**

When the bullet hits the wooden block, it transfers some of its kinetic energy to the block. The work done by the bullet is equal to the force exerted multiplied by the distance traveled. By using the formula for work done, we can calculate the average force exerted by the bullet on the block. In this case, the force is found to be 1875 Newtons.

It is important to note that this calculation assumes that the force exerted by the bullet is constant over the entire distance of penetration. In reality, the force may vary as the bullet slows down and comes to a stop within the block. Additionally, this calculation does not take into account factors such as friction, deformation of the bullet or block, or heat generated during the impact. These factors may affect the accuracy of the calculated force.

V^2 = u^2 - 2as , 2as = V^2 - u^2 ,2×a×6/100 = 0 - (150)^2 ,12a/100 = - 22500 ,a = - 2250000/12 ,avg force = ma ,= 10/1000 × 2250000/12 = 1875 N