Question

A bullet of 10 g leaves the barrel of gun with a velocity of 600 m/s. If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be :

• A. 12 Ns
• B. 3 Ns
• C. 6 Ns
• D. 36 Ns

Hint:

{Impulse} is the product of force and the time during which the force acts. It is equal to the change in momentum of an object. Mathematically, \( J = F \cdot t = \Delta p \).

Answer 1

The Correct Option is C

To find the impulse supplied to the gun when the bullet has been fired, we will use the concept of impulse and momentum. Impulse is defined as the change in momentum of an object when a force is applied over a period of time. The formula for impulse (\( J \)) is given by:

J = \Delta p = m \cdot \Delta v

where \Delta p is the change in momentum, m is the mass, and \Delta v is the change in velocity.

Given:

• Mass of the bullet, m = 10 \ \text{g} = 0.01 \ \text{kg} (since 1 g = 0.001 kg)
• Velocity of the bullet, v = 600 \ \text{m/s}
• Initial velocity of the bullet, u = 0 \ \text{m/s} (the bullet starts at rest)

The change in velocity \Delta v of the bullet can be calculated as:

\Delta v = v - u = 600 \ \text{m/s} - 0 \ \text{m/s} = 600 \ \text{m/s}

Using the impulse formula:

J = m \cdot \Delta v = 0.01 \ \text{kg} \cdot 600 \ \text{m/s} = 6 \ \text{Ns}

Thus, the impulse supplied to the gun is 6 \ \text{Ns}, which matches the correct answer.