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STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.
STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
- a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
- b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
- c)Statement -1 is True, Statement-2 is False
- d)Statement -1 is False, Statement-2 is True
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (w...
The acceleration of a body rolling down an inclined plane is given by
⇒ Acceleration of solid cylinder is more than hollow cylinder and therefore solid cylinder will reach the bottom of the inclined plane first.
∴ Statement -1 is false
• Statement - 2 In the case of rolling there will be no heat losses.
Therefore total mechanical energy remains conserved.
The potential energy therefore gets converted into kinetic energy. In both the cases since the initial potential energy is same, the final kinetic energy will also be same. Therefore statement -2 is correct.
Therefore total mechanical energy remains conserved.
The potential energy therefore gets converted into kinetic energy. In both the cases since the initial potential energy is same, the final kinetic energy will also be same. Therefore statement -2 is correct.
Most Upvoted Answer
STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (w...
Statement-1: Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.
Statement-2: By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
Explanation:
Conservation of Energy:
The principle of conservation of energy states that the total mechanical energy of a system remains constant if no external forces are acting on it. In this case, as the cylinders are rolling down the inclined plane without slipping, we can assume that no external forces are acting on them.
Rolling Motion:
When a cylinder rolls without slipping, it has both translational and rotational kinetic energy. The translational kinetic energy is given by 1/2 * mv^2, where m is the mass of the cylinder and v is its linear velocity. The rotational kinetic energy is given by 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity.
Comparison of Hollow and Solid Cylinders:
The moment of inertia of a hollow cylinder is greater than that of a solid cylinder of the same mass and dimensions. This is because most of the mass of a hollow cylinder is located on the outer rim, resulting in a larger moment of inertia compared to a solid cylinder with the same mass distributed more evenly.
Analyzing the Statements:
Statement-1 states that the hollow cylinder will reach the bottom of the inclined plane first. This is because the hollow cylinder has a larger moment of inertia compared to the solid cylinder. Due to its larger moment of inertia, it takes more energy for the hollow cylinder to start rolling and reach the same linear velocity as the solid cylinder. Therefore, the solid cylinder accelerates faster and reaches the bottom of the inclined plane first.
Statement-2 states that the total kinetic energies of both cylinders are identical when they reach the bottom of the incline. This is true because the principle of conservation of energy applies. As both cylinders have the same mass and reach the same linear velocity at the bottom of the inclined plane, their total kinetic energies will be equal.
Conclusion:
Therefore, Statement-1 is true and Statement-2 is true. However, Statement-2 is not a correct explanation for Statement-1. The reason the hollow cylinder reaches the bottom of the inclined plane first is due to its larger moment of inertia, not the conservation of energy.
Statement-2: By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
Explanation:
Conservation of Energy:
The principle of conservation of energy states that the total mechanical energy of a system remains constant if no external forces are acting on it. In this case, as the cylinders are rolling down the inclined plane without slipping, we can assume that no external forces are acting on them.
Rolling Motion:
When a cylinder rolls without slipping, it has both translational and rotational kinetic energy. The translational kinetic energy is given by 1/2 * mv^2, where m is the mass of the cylinder and v is its linear velocity. The rotational kinetic energy is given by 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity.
Comparison of Hollow and Solid Cylinders:
The moment of inertia of a hollow cylinder is greater than that of a solid cylinder of the same mass and dimensions. This is because most of the mass of a hollow cylinder is located on the outer rim, resulting in a larger moment of inertia compared to a solid cylinder with the same mass distributed more evenly.
Analyzing the Statements:
Statement-1 states that the hollow cylinder will reach the bottom of the inclined plane first. This is because the hollow cylinder has a larger moment of inertia compared to the solid cylinder. Due to its larger moment of inertia, it takes more energy for the hollow cylinder to start rolling and reach the same linear velocity as the solid cylinder. Therefore, the solid cylinder accelerates faster and reaches the bottom of the inclined plane first.
Statement-2 states that the total kinetic energies of both cylinders are identical when they reach the bottom of the incline. This is true because the principle of conservation of energy applies. As both cylinders have the same mass and reach the same linear velocity at the bottom of the inclined plane, their total kinetic energies will be equal.
Conclusion:
Therefore, Statement-1 is true and Statement-2 is true. However, Statement-2 is not a correct explanation for Statement-1. The reason the hollow cylinder reaches the bottom of the inclined plane first is due to its larger moment of inertia, not the conservation of energy.
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STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer?
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STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer?.
STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer?.
Solutions for STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice STATEMENT-1 : Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.STATEMENT-2 : By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.a)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1b)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1c)Statement -1 is True, Statement-2 is Falsed)Statement -1 is False, Statement-2 is TrueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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