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Standard XII

Physics

Work Energy Theorem

A machine gun...

Question

A machine gun is mounted on a $2000 k g$ car on a horizontal frictionless surface. At some instant, the gun fires $10$ bullets/second, each of mass $10 g$ with a velocity of $500 m s^{- 1}$ . The acceleration of the car is:

0.025 m s^{- 1}

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0.25 m s^{- 1}

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0.5 m s^{- 1}

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500 m s^{- 1}

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Solution

The correct option is A $0.025 m s^{- 1}$
$M_{c a r} = 2000 k g$
n=10 bullets/second
$m_{b} = 10 g = 0.01 k g$
$v_{b} = 500 m / s$
Momentum of each bullet= $P_{b} = m_{b} v_{b} = 0.01 \times 500 = 5 k g m s^{- 1}$
Force on car= $n P_{b} = 50 k g m s^{- 2}$
$F_{c a r} = 50 N$
$a_{c a r} = \frac{50}{2000} = \frac{1}{40} = 0.025 m s^{- 2}$

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A machine gun is mounted on a 2000kg car on a horizontal frictionless surface. At some instant, the gun fires 10 bullets/second, each of mass 10g with a velocity of 500ms−1. The acceleration of the car is:

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