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A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.?
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A train of mass M is moving with constant velocity along a straight li...
Given information:
- Train mass: M
- Mass of last compartment: m
- Distance travelled by last compartment before disconnecting: l
- Opposing force proportional to mass
Analysis:
- Initially, the train's velocity is constant.
- When the last compartment disconnects, the opposing force suddenly increases.
- The driver shuts down the engine, causing the train to decelerate.
- The opposing force on the train is proportional to its mass M.
- The opposing force on the last compartment is proportional to its mass m.
Calculations:
- Let x be the distance between the last compartment and the train when they come to rest.
- The total opposing force on the train when the last compartment disconnects is M*g, where g is the acceleration due to gravity.
- The total opposing force on the last compartment is m*g.
- When both come to rest, the total opposing force is 0.
- Using the principle of conservation of momentum, we have:
M*l = M*x + m*(l-x)
=> Ml = Mx + ml - mx
=> Ml = Mx + ml - mx
=> Ml = Mx + ml - mx
=> Ml = M(x-m)
=> x = Ml/(M-m)
Conclusion:
The distance between the last compartment and the train when they come to rest is Ml/(M-m).
- Train mass: M
- Mass of last compartment: m
- Distance travelled by last compartment before disconnecting: l
- Opposing force proportional to mass
Analysis:
- Initially, the train's velocity is constant.
- When the last compartment disconnects, the opposing force suddenly increases.
- The driver shuts down the engine, causing the train to decelerate.
- The opposing force on the train is proportional to its mass M.
- The opposing force on the last compartment is proportional to its mass m.
Calculations:
- Let x be the distance between the last compartment and the train when they come to rest.
- The total opposing force on the train when the last compartment disconnects is M*g, where g is the acceleration due to gravity.
- The total opposing force on the last compartment is m*g.
- When both come to rest, the total opposing force is 0.
- Using the principle of conservation of momentum, we have:
M*l = M*x + m*(l-x)
=> Ml = Mx + ml - mx
=> Ml = Mx + ml - mx
=> Ml = Mx + ml - mx
=> Ml = M(x-m)
=> x = Ml/(M-m)
Conclusion:
The distance between the last compartment and the train when they come to rest is Ml/(M-m).
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A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.?
Question Description
A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.?.
A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.?.
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A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.?, a detailed solution for A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.? has been provided alongside types of A train of mass M is moving with constant velocity along a straight line. Suddenly the last compartment gets disconnected. After moving a distance l, the driver realised and shuts down the engine. If the opposing force acting on the train is proportional to the mass, then show that the distance between the last compartment and the train when both of them comes to rest isMl/(M-m). Here m is the mass of last compartment. Also assume that the force of engine is constant.? theory, EduRev gives you an
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