Correct Answer - Option 2 : 3
The correct answer is option 2) i.e. 3
CONCEPT:
-
Linear momentum: Linear momentum is the impact caused due to a body in translational motion.
- The greater the mass and velocity of the moving body the more will be the impact and thus greater the momentum.
- The linear momentum of a moving object is defined mathematically as:
⇒ p = mv
Where p is the linear momentum, m is the mass of the object, and v is the velocity of the object.
- From Newton's second law of motion, the rate of change of momentum is directly proportional to the force applied by the moving body.
⇒ dp/dt ∝ F
\(⇒ \frac{dp}{dt} = \frac{d(mv)}{dt} = m\frac{dv}{dt} = ma =F\)
CALCULATION:
Given that:
Mass of each bullet, m = 40 g = 0.04 kg
Velocity of the bullet, v = 1200 m/s
Let N be the number of bullets fired in each second (\(\frac{N}{1\: s}\))
When N bullets are fired per second, the total force that can be exerted on the gun, F = 144 N
The momentum of N bullets, p = N(mv)
From Newton's second law of motion,
\(⇒ \frac{d(Nmv)}{dt} = m\times v \times\frac{N}{t} =F \)
\(⇒ 0.04\times1200\times \frac{N}{1}=144\) (∵ t = 1 s)
⇒ N = 3
