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A stone of mass 5 kg is attached to a string of 10 m length and is whirled in a horizontal circle. The string can withstand a maximum tension of 160 N. The maximum velocity of revolution that can be given to the stone without breaking the string is
- a)17.88 m/s
- b)16 m/s
- c)20 m/s
- d)19.4 m/s
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A stone of mass 5 kg is attached to a string of 10 m length and is whi...
maximum tension = (mv^2)/ r,
60 = 5*v^2/10
v = 17.88
v = 17.88
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A stone of mass 5 kg is attached to a string of 10 m length and is whi...
Given, mass of stone, m = 5 kg
Length of string, l = 10 m
Maximum tension, T = 160 N
We need to find the maximum velocity of revolution that can be given to the stone without breaking the string.
Maximum velocity of revolution:
We know that the tension in the string, T is given by:
T = (mv²) / r
where m is the mass of the stone, v is the velocity of the stone and r is the radius of the circle.
Finding the radius:
The length of the string, l is equal to the circumference of the circle, so:
l = 2πr
=> r = l / (2π)
=> r = 10 / (2π) = 1.59 m
Finding the maximum velocity:
Substituting the values in the tension equation, we get:
T = (mv²) / r
=> v² = (Tr) / m
=> v = √[(Tr) / m]
Now, substituting the given values, we get:
v = √[(160 × 1.59) / 5]
=> v = 17.88 m/s
Therefore, the maximum velocity of revolution that can be given to the stone without breaking the string is 17.88 m/s.
Length of string, l = 10 m
Maximum tension, T = 160 N
We need to find the maximum velocity of revolution that can be given to the stone without breaking the string.
Maximum velocity of revolution:
We know that the tension in the string, T is given by:
T = (mv²) / r
where m is the mass of the stone, v is the velocity of the stone and r is the radius of the circle.
Finding the radius:
The length of the string, l is equal to the circumference of the circle, so:
l = 2πr
=> r = l / (2π)
=> r = 10 / (2π) = 1.59 m
Finding the maximum velocity:
Substituting the values in the tension equation, we get:
T = (mv²) / r
=> v² = (Tr) / m
=> v = √[(Tr) / m]
Now, substituting the given values, we get:
v = √[(160 × 1.59) / 5]
=> v = 17.88 m/s
Therefore, the maximum velocity of revolution that can be given to the stone without breaking the string is 17.88 m/s.
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A stone of mass 5 kg is attached to a string of 10 m length and is whirled in a horizontal circle. The string can withstand a maximum tension of 160 N. The maximum velocity of revolution that can be given to the stone without breaking the string isa)17.88 m/sb)16 m/sc)20 m/sd)19.4 m/sCorrect answer is option 'A'. Can you explain this answer?
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