Question

A gun fires N bullets per minute. The mass of each bullet is 10g and every bullet travels With a speed of 600m/s. If the power delivered by the gun is 9000W,the value of N is:

• A. 300
• B. 400
• C. 360
• D. 420
• E. 250

Answer 1

The Correct Option is A

Given:

• Mass of each bullet, \( m = 10 \, \text{g} = 0.01 \, \text{kg} \)
• Speed of each bullet, \( v = 600 \, \text{m/s} \)
• Power delivered by gun, \( P = 9000 \, \text{W} \)
• Number of bullets fired per minute = \( N \)

Step 1: Calculate Kinetic Energy per Bullet

The kinetic energy (KE) of one bullet is:

\[ \text{KE} = \frac{1}{2} m v^2 = \frac{1}{2} \times 0.01 \times (600)^2 = 1800 \, \text{J} \]

Step 2: Determine Total Energy per Minute

Power is energy per unit time. For \( N \) bullets per minute (60 seconds):

\[ P = \frac{N \times \text{KE}}{60} \]

Rearrange to solve for \( N \):

\[ N = \frac{P \times 60}{\text{KE}} = \frac{9000 \times 60}{1800} = 300 \]

Conclusion:

The number of bullets fired per minute, \( N \), is 300.

Answer: \(\boxed{A}\)

Answer 2

The correct option is (A): 300
The formula for Power(P) is:
\(P = \frac{W}{t}\)
Where W is the work done and t is the time taken.
The work done in this case is the kinetic energy KE of one bullet, which is given by:
 

\[KE = \frac{1}{2} m v^2\]

Where m is the mass of the bullet and v is its velocity.
Substituting the given values:
 

\[KE = \frac{1}{2} \times 0.01 \, \text{kg} \times (600 \, \text{m/s})^2\]

 

\[KE = 1800 \, \text{J}\]

Now, since the power P is given as 9000W, we can rewrite the power formula as:
 

\[9000 = \frac{1800 \times N}{60}\]

Where N is the number of bullets fired per minute.
 

\[9000 \times 60 = 1800 \times N\]\[540000 = 1800N\]

 

\[N = \frac{540000}{1800}\]

 

\[N = 300\]

Thus, the number of bullets fired per minute is N=300