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A thin uniform rod AB of mass m and length L is hinged at one end A to the level floor. Initially it stands vertically and is allowed to fall freely to the floor in the vertical plane. The angular velocity of the rod, when its end B strikes the floor is
- a)mg/L
- b)(mg/3L)1/2
- c)g/ L
- d)(3g/L)1/2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A thin uniform rod AB of mass m and length L is hinged at one end A to...
Since the centre of gravity of the rod is at its centre,
the loss in PE when its end B strikes the floor = mg ( L/2 ) = 1/2 mg L
Gain in KE = 1/2 Iω2
where I is the moment of intertia of the rod about an axis passing through its end and perpendicular to its length
which is given by I = 1/3 mL2
Now gain in KE = loss in PE. i.e.
1/2 x 1/3 mL2 x ω2 = 1/2 mgL
which gives ω = √3g/L
the loss in PE when its end B strikes the floor = mg ( L/2 ) = 1/2 mg L
Gain in KE = 1/2 Iω2
where I is the moment of intertia of the rod about an axis passing through its end and perpendicular to its length
which is given by I = 1/3 mL2
Now gain in KE = loss in PE. i.e.
1/2 x 1/3 mL2 x ω2 = 1/2 mgL
which gives ω = √3g/L
Most Upvoted Answer
A thin uniform rod AB of mass m and length L is hinged at one end A to...
Free Fall of the Rod
- As the rod falls freely under gravity, the torque acting on it about point A is given by τ = Iα, where I is the moment of inertia of the rod and α is the angular acceleration.
- The moment of inertia of a thin rod rotating about one end is I = mL²/3.
- The torque causing the angular acceleration is τ = mgl sinθ, where θ is the angle made by the rod with the vertical.
- Solving these equations, we get α = 3g/L.
Angular Velocity at Impact
- Using the kinematic equation ω² = ω₀² + 2αθ, where ω₀ is the initial angular velocity and θ is the final angular displacement (90 degrees in this case).
- As the rod starts from rest, ω₀ = 0, and θ = 90 degrees = π/2 radians.
- Substituting the values, we get ω = (2αθ)^(1/2) = (2 * 3g/L * π/2)^(1/2) = (3g/L)^(1/2).
Therefore, the angular velocity of the rod when its end B strikes the floor is (3g/L)^(1/2), which corresponds to option 'D'.
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A thin uniform rod AB of mass m and length L is hinged at one end A to the level floor. Initially it stands vertically and is allowed to fall freely to the floor in the vertical plane. The angular velocity of the rod, when its end B strikes the floor isa)mg/Lb)(mg/3L)1/2 c)g/ Ld)(3g/L)1/2Correct answer is option 'D'. Can you explain this answer?
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A thin uniform rod AB of mass m and length L is hinged at one end A to the level floor. Initially it stands vertically and is allowed to fall freely to the floor in the vertical plane. The angular velocity of the rod, when its end B strikes the floor isa)mg/Lb)(mg/3L)1/2 c)g/ Ld)(3g/L)1/2Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A thin uniform rod AB of mass m and length L is hinged at one end A to the level floor. Initially it stands vertically and is allowed to fall freely to the floor in the vertical plane. The angular velocity of the rod, when its end B strikes the floor isa)mg/Lb)(mg/3L)1/2 c)g/ Ld)(3g/L)1/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin uniform rod AB of mass m and length L is hinged at one end A to the level floor. Initially it stands vertically and is allowed to fall freely to the floor in the vertical plane. The angular velocity of the rod, when its end B strikes the floor isa)mg/Lb)(mg/3L)1/2 c)g/ Ld)(3g/L)1/2Correct answer is option 'D'. Can you explain this answer?.
A thin uniform rod AB of mass m and length L is hinged at one end A to the level floor. Initially it stands vertically and is allowed to fall freely to the floor in the vertical plane. The angular velocity of the rod, when its end B strikes the floor isa)mg/Lb)(mg/3L)1/2 c)g/ Ld)(3g/L)1/2Correct answer is option 'D'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A thin uniform rod AB of mass m and length L is hinged at one end A to the level floor. Initially it stands vertically and is allowed to fall freely to the floor in the vertical plane. The angular velocity of the rod, when its end B strikes the floor isa)mg/Lb)(mg/3L)1/2 c)g/ Ld)(3g/L)1/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thin uniform rod AB of mass m and length L is hinged at one end A to the level floor. Initially it stands vertically and is allowed to fall freely to the floor in the vertical plane. The angular velocity of the rod, when its end B strikes the floor isa)mg/Lb)(mg/3L)1/2 c)g/ Ld)(3g/L)1/2Correct answer is option 'D'. Can you explain this answer?.
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