Answer
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Hint:In order to solve this question, we will use the concept of Newton’s second law of motion which states that, force on a body is equal to rate of change in momentum of the body, where momentum is defined as the product of mass and velocity of the body.
Formula used:
Mathematically Newton's second law is written as $F = \dfrac{p}{t}$ where $p$ denotes momentum of the body and defined as $p = m \times v$ .
Complete step by step answer:
According to the question we have,
Mass of the bullet is $m = 35g = 0.035\,Kg$.
Velocity of the bullet firing is $v = 400\,m{s^{ - 1}}$.
Total number of bullets fired in one minute is $n = 400$.
Time taken to fire these bullets is one minute $t = 60\,s$.
Now, according to the definition of force, we need to find the ratio of momentum and time taken. So, momentum of the single bullet is $p = mv$
Momentum of total bullets is $p' = nmv$
$p' = 400 \times 400 \times 0.035$
$\Rightarrow p' = 5600\,Kgm{s^{ - 1}}$
Now, using formula of force we have,
$F = \dfrac{{p'}}{t}$
\[\Rightarrow F = \dfrac{{5600}}{{60}}\]
$\therefore F = 93.3N$
Hence, the average force needed for fire gun to stay in its position is $F = 93.3\,N$.
Note: It should be remembered that, basic units of conversions are as $1\,g = 0.001\,Kg$ and $1\min = 60\sec $ and the SI unit for force is newton and $1\,N$ is defined as the product of $1\,kg$ mass of a body moving with an acceleration of $1\,m{\sec ^{ - 2}}$, force and momentum are both a vector quantity such that they have magnitude a well as direction and in given question the direction of momentum of bullet and momentum on fire gun is opposite which makes fire gun stable in its respective position.
Formula used:
Mathematically Newton's second law is written as $F = \dfrac{p}{t}$ where $p$ denotes momentum of the body and defined as $p = m \times v$ .
Complete step by step answer:
According to the question we have,
Mass of the bullet is $m = 35g = 0.035\,Kg$.
Velocity of the bullet firing is $v = 400\,m{s^{ - 1}}$.
Total number of bullets fired in one minute is $n = 400$.
Time taken to fire these bullets is one minute $t = 60\,s$.
Now, according to the definition of force, we need to find the ratio of momentum and time taken. So, momentum of the single bullet is $p = mv$
Momentum of total bullets is $p' = nmv$
$p' = 400 \times 400 \times 0.035$
$\Rightarrow p' = 5600\,Kgm{s^{ - 1}}$
Now, using formula of force we have,
$F = \dfrac{{p'}}{t}$
\[\Rightarrow F = \dfrac{{5600}}{{60}}\]
$\therefore F = 93.3N$
Hence, the average force needed for fire gun to stay in its position is $F = 93.3\,N$.
Note: It should be remembered that, basic units of conversions are as $1\,g = 0.001\,Kg$ and $1\min = 60\sec $ and the SI unit for force is newton and $1\,N$ is defined as the product of $1\,kg$ mass of a body moving with an acceleration of $1\,m{\sec ^{ - 2}}$, force and momentum are both a vector quantity such that they have magnitude a well as direction and in given question the direction of momentum of bullet and momentum on fire gun is opposite which makes fire gun stable in its respective position.
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