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A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s.Each bullet has a mass of 10 g with a muzzle velocity of 800 ms–1. The final velocity acquired by the person and the average force exerted on the person are [NEET Kar. 2013]
- a)–1.6 ms–1; 8 N
- b)–0.08 ms–1; 16 N
- c)– 0.8 ms–1; 16 N
- d)–1.6 ms–1; 16 N
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A person holding a rifle (mass of person and rifle together is 100 kg)...
We have to use the Law of momentum conservation:
P ( initial ) = P ( final )
0 = n · m · u + ( M - n · m ) · v
where: n = 10, m = 10 g = 0.01 kg, u = 800 m/s, M = 100 kg.
0 = 10 · 0.01 kg · 800 m/s + ( 100 kg - 10 · 0.01 kg ) · v
v = - 80 kgm/s / 99.9 kgm/s
v = 0.8 m/s
Then : F = Δ P / Δ t = ( 10 · 0.01 kg · 800 m/s ) : 5 s = 16 N
Answer: The average force exerted on the person is 16 N.
Most Upvoted Answer
A person holding a rifle (mass of person and rifle together is 100 kg)...
-1
To solve this problem, we need to use the principle of conservation of momentum. The total momentum of the system (person, rifle, and bullets) before firing is zero, since everything is at rest. After firing, the momentum of the bullets is given by:
p_bullets = m_bullet * v_bullet
where m_bullet is the mass of each bullet (10 g = 0.01 kg) and v_bullet is the muzzle velocity (800 m/s). Since 10 bullets are fired, the total momentum of the bullets is:
p_bullets_total = 10 * m_bullet * v_bullet = 10 * 0.01 kg * 800 m/s = 8 kg m/s
According to the principle of conservation of momentum, the total momentum of the system after firing must also be zero. Therefore, the momentum of the person and rifle after firing must be:
p_person_rifle = - p_bullets_total
where the negative sign indicates that the person and rifle move in the opposite direction to the bullets. The velocity of the person and rifle after firing can be calculated using:
p_person_rifle = (m_person + m_rifle) * v_person_rifle
where m_person and m_rifle are the masses of the person and rifle, respectively (we assume they are equal), and v_person_rifle is their common velocity. Solving for v_person_rifle, we get:
v_person_rifle = - p_bullets_total / (m_person + m_rifle) = - 8 kg m/s / 100 kg = - 0.08 m/s
This means that the person and rifle move backwards with a velocity of 0.08 m/s after firing. Note that this is a very small velocity, since the mass of the person and rifle is much larger than the mass of the bullets.
To solve this problem, we need to use the principle of conservation of momentum. The total momentum of the system (person, rifle, and bullets) before firing is zero, since everything is at rest. After firing, the momentum of the bullets is given by:
p_bullets = m_bullet * v_bullet
where m_bullet is the mass of each bullet (10 g = 0.01 kg) and v_bullet is the muzzle velocity (800 m/s). Since 10 bullets are fired, the total momentum of the bullets is:
p_bullets_total = 10 * m_bullet * v_bullet = 10 * 0.01 kg * 800 m/s = 8 kg m/s
According to the principle of conservation of momentum, the total momentum of the system after firing must also be zero. Therefore, the momentum of the person and rifle after firing must be:
p_person_rifle = - p_bullets_total
where the negative sign indicates that the person and rifle move in the opposite direction to the bullets. The velocity of the person and rifle after firing can be calculated using:
p_person_rifle = (m_person + m_rifle) * v_person_rifle
where m_person and m_rifle are the masses of the person and rifle, respectively (we assume they are equal), and v_person_rifle is their common velocity. Solving for v_person_rifle, we get:
v_person_rifle = - p_bullets_total / (m_person + m_rifle) = - 8 kg m/s / 100 kg = - 0.08 m/s
This means that the person and rifle move backwards with a velocity of 0.08 m/s after firing. Note that this is a very small velocity, since the mass of the person and rifle is much larger than the mass of the bullets.
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A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s.Each bullet has a mass of 10 g with a muzzle velocity of 800 ms–1. The final velocity acquired by the person and the average force exerted on the person are [NEET Kar. 2013]a)–1.6 ms–1; 8 Nb)–0.08 ms–1; 16 Nc)– 0.8 ms–1; 16Nd)–1.6 ms–1; 16 NCorrect answer is option 'C'. Can you explain this answer?
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A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s.Each bullet has a mass of 10 g with a muzzle velocity of 800 ms–1. The final velocity acquired by the person and the average force exerted on the person are [NEET Kar. 2013]a)–1.6 ms–1; 8 Nb)–0.08 ms–1; 16 Nc)– 0.8 ms–1; 16Nd)–1.6 ms–1; 16 NCorrect answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s.Each bullet has a mass of 10 g with a muzzle velocity of 800 ms–1. The final velocity acquired by the person and the average force exerted on the person are [NEET Kar. 2013]a)–1.6 ms–1; 8 Nb)–0.08 ms–1; 16 Nc)– 0.8 ms–1; 16Nd)–1.6 ms–1; 16 NCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s.Each bullet has a mass of 10 g with a muzzle velocity of 800 ms–1. The final velocity acquired by the person and the average force exerted on the person are [NEET Kar. 2013]a)–1.6 ms–1; 8 Nb)–0.08 ms–1; 16 Nc)– 0.8 ms–1; 16Nd)–1.6 ms–1; 16 NCorrect answer is option 'C'. Can you explain this answer?.
A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s.Each bullet has a mass of 10 g with a muzzle velocity of 800 ms–1. The final velocity acquired by the person and the average force exerted on the person are [NEET Kar. 2013]a)–1.6 ms–1; 8 Nb)–0.08 ms–1; 16 Nc)– 0.8 ms–1; 16Nd)–1.6 ms–1; 16 NCorrect answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s.Each bullet has a mass of 10 g with a muzzle velocity of 800 ms–1. The final velocity acquired by the person and the average force exerted on the person are [NEET Kar. 2013]a)–1.6 ms–1; 8 Nb)–0.08 ms–1; 16 Nc)– 0.8 ms–1; 16Nd)–1.6 ms–1; 16 NCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person holding a rifle (mass of person and rifle together is 100 kg) stands on a smooth surface and fires 10 shots horizontally, in 5 s.Each bullet has a mass of 10 g with a muzzle velocity of 800 ms–1. The final velocity acquired by the person and the average force exerted on the person are [NEET Kar. 2013]a)–1.6 ms–1; 8 Nb)–0.08 ms–1; 16 Nc)– 0.8 ms–1; 16Nd)–1.6 ms–1; 16 NCorrect answer is option 'C'. Can you explain this answer?.
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