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A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 m−s⁻2, then the maximum angular velocity of the stone will be
  • a)
    2 rad-s⁻1
  • b)
    4 rad-s⁻1
  • c)
    8 rad-s⁻1
  • d)
    16 rad-s⁻1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A weightless thread can bear tension upto 37 N. A stone of mass 500 g ...
Maximum tension will act when the stone is at the lowest position so costheta will be zero in mgcostheta
T-mgcostheta=m×r×w^2
just put all the values of T,m,r,g and you will get the answer w=4
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Community Answer
A weightless thread can bear tension upto 37 N. A stone of mass 500 g ...
Given data:
- Weightless thread tension capacity: 37 N
- Mass of stone: 500 g
- Radius of circular path: 4 m
- Acceleration due to gravity: 10 m/s^2

Calculating maximum tension:
- The weight of the stone is given by W = mg, where m = 0.5 kg and g = 10 m/s^2.
- W = 0.5 kg * 10 m/s^2 = 5 N
- The tension in the thread when the stone is at the bottom of the circular path is T = W + mv^2/r, where v is the velocity of the stone.
- T = 5 N + 0.5 kg * (v^2/4 m) = 37 N (maximum tension capacity)
- Solving for v^2, we get v^2 = 4 * (37 - 5) = 128
- Taking the square root of both sides, we get v = 8 m/s

Calculating maximum angular velocity:
- The angular velocity of the stone can be calculated using the formula v = rω, where v is the linear velocity, r is the radius, and ω is the angular velocity.
- Substituting the values, 8 = 4 * ω
- Therefore, ω = 8/4 = 2 rad/s
Therefore, the maximum angular velocity of the stone will be 2 rad/s (option B).
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A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. If g = 10 m−s2, then the maximum angular velocity of the stone will bea)2 rad-s1b)4 rad-s1c)8 rad-s1d)16 rad-s1Correct answer is option 'B'. Can you explain this answer?
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