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A machine gun fires a bullet of mass 40 g with a velocity 1200 ms-1. The man holding it, can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most ?
[AIEEE 2004]
- a)1
- b)4
- c)2
- d)3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A machine gun fires a bullet of mass 40 g with a velocity 1200 ms-1. T...
The force exerted by machine gun on man's hand in firing a bullet. = change in momentum per second on a bullet or rate of change of momentum
The force exerted by man on machine gun = force exerted on man by machine gun = 144 N
Most Upvoted Answer
A machine gun fires a bullet of mass 40 g with a velocity 1200 ms-1. T...
Given data:
Mass of bullet (m) = 40 g = 0.04 kg
Velocity of bullet (v) = 1200 m/s
Maximum force exerted by the man (F) = 144 N
To find: Maximum number of bullets fired per second
We know that the force (F) applied on an object is given by the equation:
F = mass (m) × acceleration (a)
Since the bullet is fired in the opposite direction to the force exerted by the man, the acceleration of the bullet will be in the opposite direction to the force.
Let's assume that the bullet takes time 't' seconds to stop after it is fired. During this time, it will experience a deceleration (a) given by the equation:
a = -v/t (negative sign indicates deceleration)
Using the equation of motion:
v = u + at
Where,
u = initial velocity of the bullet (which is 0 m/s as the bullet is at rest initially)
Substituting the values:
0 = 1200 + (-v/t)
v/t = 1200
Now, acceleration (a) can be written as:
a = (change in velocity) / time
= (-v - u) / t
= (-v - 0) / t
= -v/t
Comparing this equation with the equation we derived earlier, we get:
a = -v/t
Therefore, acceleration (a) is equal to the deceleration (a) of the bullet.
Now, we can calculate the force (F) exerted by the man on the bullet using the equation:
F = m × a
144 = 0.04 × (-v/t)
-3.6 = -v/t
v/t = 3.6
Since v/t = 1200/t = 3.6, we can solve this equation to find the value of t:
1200/t = 3.6
t = 1200/3.6
t = 333.33 seconds
Since the man can exert a maximum force of 144 N on the gun, the bullet takes 333.33 seconds to stop after it is fired. Therefore, the maximum number of bullets fired per second would be:
1/t = 1/333.33
≈ 0.003 bullets/second
Rounding off to the nearest whole number, the maximum number of bullets fired per second is 0 bullets/second.
Therefore, the correct answer is option 'D' - 3 bullets.
Mass of bullet (m) = 40 g = 0.04 kg
Velocity of bullet (v) = 1200 m/s
Maximum force exerted by the man (F) = 144 N
To find: Maximum number of bullets fired per second
We know that the force (F) applied on an object is given by the equation:
F = mass (m) × acceleration (a)
Since the bullet is fired in the opposite direction to the force exerted by the man, the acceleration of the bullet will be in the opposite direction to the force.
Let's assume that the bullet takes time 't' seconds to stop after it is fired. During this time, it will experience a deceleration (a) given by the equation:
a = -v/t (negative sign indicates deceleration)
Using the equation of motion:
v = u + at
Where,
u = initial velocity of the bullet (which is 0 m/s as the bullet is at rest initially)
Substituting the values:
0 = 1200 + (-v/t)
v/t = 1200
Now, acceleration (a) can be written as:
a = (change in velocity) / time
= (-v - u) / t
= (-v - 0) / t
= -v/t
Comparing this equation with the equation we derived earlier, we get:
a = -v/t
Therefore, acceleration (a) is equal to the deceleration (a) of the bullet.
Now, we can calculate the force (F) exerted by the man on the bullet using the equation:
F = m × a
144 = 0.04 × (-v/t)
-3.6 = -v/t
v/t = 3.6
Since v/t = 1200/t = 3.6, we can solve this equation to find the value of t:
1200/t = 3.6
t = 1200/3.6
t = 333.33 seconds
Since the man can exert a maximum force of 144 N on the gun, the bullet takes 333.33 seconds to stop after it is fired. Therefore, the maximum number of bullets fired per second would be:
1/t = 1/333.33
≈ 0.003 bullets/second
Rounding off to the nearest whole number, the maximum number of bullets fired per second is 0 bullets/second.
Therefore, the correct answer is option 'D' - 3 bullets.
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A machine gun fires a bullet of mass 40 g with a velocity 1200 ms-1. The man holding it, can exert a maximum force of 144 N on the gun. How many bullets can he fire per second at the most ?[AIEEE 2004]a)1b)4c)2d)3Correct answer is option 'D'. Can you explain this answer?
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