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On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikes
another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the
impact, if both the vehicles stick together, the common velocity (in m/s) with which both the
vehicles will move together is __________
another vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After the
impact, if both the vehicles stick together, the common velocity (in m/s) with which both the
vehicles will move together is __________
(Important : you should answer only the numeric value)
Correct answer is '20'. Can you explain this answer?
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On a single straight track, a vehicle of mass 500 kg moving with a vel...
Given:
- Mass of the first vehicle (m1) = 500 kg
- Initial velocity of the first vehicle (u1) = 25 m/s
- Mass of the second vehicle (m2) = 250 kg
- Initial velocity of the second vehicle (u2) = 10 m/s
To find:
- Common velocity (v) with which both vehicles will move together after the impact
Momentum:
Momentum is the product of mass and velocity of an object. It is given by the equation:
Momentum (p) = mass (m) × velocity (v)
Conservation of Momentum:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision, provided no external forces act on the system.
Mathematically, it can be expressed as:
Total momentum before collision = Total momentum after collision
(m1 × u1) + (m2 × u2) = (m1 + m2) × v
Substituting the given values:
(500 kg × 25 m/s) + (250 kg × 10 m/s) = (500 kg + 250 kg) × v
Simplifying the equation:
12500 kg·m/s + 2500 kg·m/s = 750 kg × v
15000 kg·m/s = 750 kg × v
Dividing both sides of the equation by 750 kg:
v = 15000 kg·m/s / 750 kg
v = 20 m/s
Therefore, the common velocity with which both vehicles will move together after the impact is 20 m/s.
- Mass of the first vehicle (m1) = 500 kg
- Initial velocity of the first vehicle (u1) = 25 m/s
- Mass of the second vehicle (m2) = 250 kg
- Initial velocity of the second vehicle (u2) = 10 m/s
To find:
- Common velocity (v) with which both vehicles will move together after the impact
Explanation:
Momentum:
Momentum is the product of mass and velocity of an object. It is given by the equation:
Momentum (p) = mass (m) × velocity (v)
Conservation of Momentum:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision, provided no external forces act on the system.
Mathematically, it can be expressed as:
Total momentum before collision = Total momentum after collision
(m1 × u1) + (m2 × u2) = (m1 + m2) × v
Substituting the given values:
(500 kg × 25 m/s) + (250 kg × 10 m/s) = (500 kg + 250 kg) × v
Simplifying the equation:
12500 kg·m/s + 2500 kg·m/s = 750 kg × v
15000 kg·m/s = 750 kg × v
Dividing both sides of the equation by 750 kg:
v = 15000 kg·m/s / 750 kg
v = 20 m/s
Therefore, the common velocity with which both vehicles will move together after the impact is 20 m/s.
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On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikesanother vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After theimpact, if both the vehicles stick together, the common velocity (in m/s) with which both thevehicles will move together is __________(Important : you should answer only the numeric value)Correct answer is '20'. Can you explain this answer?
Question Description
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On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikesanother vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After theimpact, if both the vehicles stick together, the common velocity (in m/s) with which both thevehicles will move together is __________(Important : you should answer only the numeric value)Correct answer is '20'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikesanother vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After theimpact, if both the vehicles stick together, the common velocity (in m/s) with which both thevehicles will move together is __________(Important : you should answer only the numeric value)Correct answer is '20'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On a single straight track, a vehicle of mass 500 kg moving with a velocity of 25 m/s strikesanother vehicle of mass 250 kg moving with a velocity 10 m/s in the same direction. After theimpact, if both the vehicles stick together, the common velocity (in m/s) with which both thevehicles will move together is __________(Important : you should answer only the numeric value)Correct answer is '20'. Can you explain this answer?.
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