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A bar of length l carrying a small mass m at one of its ends rotates with a uniform angular speed ω in a vertical plane about the mid-point of the bar. During the rotation, at some instant of time when the bar is horizontal, the mass is detached from the bar but the bar continues to rotate with same ω. The mass moves vertically up, comes back and reches the bar at the same point. At that place, the acceleration due to gravity is g.
  • a)
    This is possible if the quantity ω2L/2πg is an integer
  • b)
    The total time of flight of the mass is proportional to ω2
  • c)
    The total distance travelled by the mass in air is proportional to ω2
  • d)
    The total distance travelled by the mass in air and its total time of flight are both independent on its mass.
Correct answer is option 'A,C,D'. Can you explain this answer?
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A bar of length l carrying a small mass m at one of its ends rotates w...
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A bar of length l carrying a small mass m at one of its ends rotates w...
Let's assume that the bar is rotating about an axis passing through its center of mass. We can also assume that the bar is massless, so all the mass is concentrated at the end where the small mass is located.

To find the angular speed, we can use the formula:

angular speed (ω) = linear speed (v) / radius (r)

Since the bar is rotating uniformly, the linear speed of the small mass is constant. Let's call this linear speed v.

The radius of rotation (r) is the distance from the center of mass of the bar to the small mass. Let's call this distance d.

Since the bar is rotating, we can assume that the small mass is moving in a circle of radius d. The circumference of this circle is equal to the length of the bar (l).

Therefore, we can write the equation:

2πd = l

Solving for d, we get:

d = l / (2π)

Now, we can substitute this value of d into the formula for angular speed:

ω = v / d = v / (l / (2π))

Simplifying, we get:

ω = 2πv / l

Therefore, the angular speed of the bar is given by:

ω = 2πv / l
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A bar of length l carrying a small mass m at one of its ends rotates with a uniform angular speed ω in a vertical plane about the mid-point of the bar. During the rotation, at some instant of time when the bar is horizontal, the mass is detached from the bar but the bar continues to rotate with same ω. The mass moves vertically up, comes back and reches the bar at the same point. At that place, the acceleration due to gravity is g.a)This is possible if the quantityω2L/2πg is an integerb)The total time of flight of the mass is proportional to ω2c)The total distance travelled by the mass in air is proportional to ω2d)The total distance travelled by the mass in air and its total time of flight are both independent on its mass.Correct answer is option 'A,C,D'. Can you explain this answer?
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A bar of length l carrying a small mass m at one of its ends rotates with a uniform angular speed ω in a vertical plane about the mid-point of the bar. During the rotation, at some instant of time when the bar is horizontal, the mass is detached from the bar but the bar continues to rotate with same ω. The mass moves vertically up, comes back and reches the bar at the same point. At that place, the acceleration due to gravity is g.a)This is possible if the quantityω2L/2πg is an integerb)The total time of flight of the mass is proportional to ω2c)The total distance travelled by the mass in air is proportional to ω2d)The total distance travelled by the mass in air and its total time of flight are both independent on its mass.Correct answer is option 'A,C,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 A bar of length l carrying a small mass m at one of its ends rotates with a uniform angular speed ω in a vertical plane about the mid-point of the bar. During the rotation, at some instant of time when the bar is horizontal, the mass is detached from the bar but the bar continues to rotate with same ω. The mass moves vertically up, comes back and reches the bar at the same point. At that place, the acceleration due to gravity is g.a)This is possible if the quantityω2L/2πg is an integerb)The total time of flight of the mass is proportional to ω2c)The total distance travelled by the mass in air is proportional to ω2d)The total distance travelled by the mass in air and its total time of flight are both independent on its mass.Correct answer is option 'A,C,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 A bar of length l carrying a small mass m at one of its ends rotates with a uniform angular speed ω in a vertical plane about the mid-point of the bar. During the rotation, at some instant of time when the bar is horizontal, the mass is detached from the bar but the bar continues to rotate with same ω. The mass moves vertically up, comes back and reches the bar at the same point. At that place, the acceleration due to gravity is g.a)This is possible if the quantityω2L/2πg is an integerb)The total time of flight of the mass is proportional to ω2c)The total distance travelled by the mass in air is proportional to ω2d)The total distance travelled by the mass in air and its total time of flight are both independent on its mass.Correct answer is option 'A,C,D'. Can you explain this answer?.
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