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A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is resolved in a circular path of radius 2 m in a vertical plane. if g = 10 m/s2, then the maximum angular velocity of the stone will be
- a)5 rad/s
- b)30 rad/s
- c)60 rad/s
- d)10 rad/s
Correct answer is option 'A'. Can you explain this answer?
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A weightless thread can support tension upto 30 N. A stone of mass 0.5...
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A weightless thread can support tension upto 30 N. A stone of mass 0.5...
The maximum tension that a weightless thread can support is given as 30 N. We need to determine the maximum angular velocity of a stone tied to this thread, which is resolved in a circular path of radius 2 m in a vertical plane, assuming the acceleration due to gravity (g) to be 10 m/s^2.
Let's solve this problem step by step:
1. Determine the force acting on the stone:
The force acting on the stone is the tension in the thread, which can support a maximum tension of 30 N. Therefore, the force acting on the stone can be a maximum of 30 N.
2. Determine the weight of the stone:
The weight of the stone is given by the formula: weight = mass * acceleration due to gravity.
Given that the mass of the stone is 0.5 kg and acceleration due to gravity is 10 m/s^2, we can calculate:
Weight = 0.5 kg * 10 m/s^2 = 5 N.
3. Determine the net force on the stone:
The net force on the stone is the difference between the force acting on the stone and its weight. Therefore, the net force can be calculated as:
Net force = Force - Weight = 30 N - 5 N = 25 N.
4. Determine the centripetal force:
The centripetal force acting on the stone is given by the formula: centripetal force = mass * (angular velocity)^2 * radius.
Since the thread is weightless, the only force acting on the stone is the tension in the thread, which provides the centripetal force.
Therefore, the centripetal force is given by the net force, which is 25 N.
5. Calculate the maximum angular velocity:
Using the formula for centripetal force, we can rearrange it to solve for the maximum angular velocity:
centripetal force = mass * (angular velocity)^2 * radius
25 N = 0.5 kg * (angular velocity)^2 * 2 m
Simplifying the equation, we get:
25 N = 1 kg * (angular velocity)^2
Dividing both sides by 1 kg, we have:
25 m^2/s^2 = (angular velocity)^2
Taking the square root of both sides, we get:
5 m/s = angular velocity
Therefore, the maximum angular velocity of the stone is 5 rad/s, which corresponds to option 'A'.
Let's solve this problem step by step:
1. Determine the force acting on the stone:
The force acting on the stone is the tension in the thread, which can support a maximum tension of 30 N. Therefore, the force acting on the stone can be a maximum of 30 N.
2. Determine the weight of the stone:
The weight of the stone is given by the formula: weight = mass * acceleration due to gravity.
Given that the mass of the stone is 0.5 kg and acceleration due to gravity is 10 m/s^2, we can calculate:
Weight = 0.5 kg * 10 m/s^2 = 5 N.
3. Determine the net force on the stone:
The net force on the stone is the difference between the force acting on the stone and its weight. Therefore, the net force can be calculated as:
Net force = Force - Weight = 30 N - 5 N = 25 N.
4. Determine the centripetal force:
The centripetal force acting on the stone is given by the formula: centripetal force = mass * (angular velocity)^2 * radius.
Since the thread is weightless, the only force acting on the stone is the tension in the thread, which provides the centripetal force.
Therefore, the centripetal force is given by the net force, which is 25 N.
5. Calculate the maximum angular velocity:
Using the formula for centripetal force, we can rearrange it to solve for the maximum angular velocity:
centripetal force = mass * (angular velocity)^2 * radius
25 N = 0.5 kg * (angular velocity)^2 * 2 m
Simplifying the equation, we get:
25 N = 1 kg * (angular velocity)^2
Dividing both sides by 1 kg, we have:
25 m^2/s^2 = (angular velocity)^2
Taking the square root of both sides, we get:
5 m/s = angular velocity
Therefore, the maximum angular velocity of the stone is 5 rad/s, which corresponds to option 'A'.
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A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is resolved in a circular path of radius 2 m in a vertical plane. if g = 10 m/s2, then the maximum angular velocity of the stone will bea)5 rad/sb)30 rad/sc)60 rad/sd)10 rad/sCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is resolved in a circular path of radius 2 m in a vertical plane. if g = 10 m/s2, then the maximum angular velocity of the stone will bea)5 rad/sb)30 rad/sc)60 rad/sd)10 rad/sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is resolved in a circular path of radius 2 m in a vertical plane. if g = 10 m/s2, then the maximum angular velocity of the stone will bea)5 rad/sb)30 rad/sc)60 rad/sd)10 rad/sCorrect answer is option 'A'. Can you explain this answer?.
A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is resolved in a circular path of radius 2 m in a vertical plane. if g = 10 m/s2, then the maximum angular velocity of the stone will bea)5 rad/sb)30 rad/sc)60 rad/sd)10 rad/sCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is resolved in a circular path of radius 2 m in a vertical plane. if g = 10 m/s2, then the maximum angular velocity of the stone will bea)5 rad/sb)30 rad/sc)60 rad/sd)10 rad/sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A weightless thread can support tension upto 30 N. A stone of mass 0.5 kg is tied to it and is resolved in a circular path of radius 2 m in a vertical plane. if g = 10 m/s2, then the maximum angular velocity of the stone will bea)5 rad/sb)30 rad/sc)60 rad/sd)10 rad/sCorrect answer is option 'A'. Can you explain this answer?.
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