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A body of mass 10 kg is rotated in vertical circle of radius 4 cm at constant angular velocity of 5 rad/ sec. The maximum tension in the string is- (a) 100 N (b) 600 N (c) 110 N (d) 1100 N Ans. (c) How?
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A body of mass 10 kg is rotated in vertical circle of radius 4 cm at c...
Given:
- Mass of the body (m) = 10 kg
- Radius of the circle (r) = 4 cm = 0.04 m
- Angular velocity (ω) = 5 rad/s
To find:
- Maximum tension in the string
Assumptions:
- We assume the string to be massless and inextensible.
- We neglect air resistance and friction.
Formula:
The tension in the string at the highest point of the vertical circle can be calculated using the following formula:
T = m * (v² / r) + m * g
where:
T = tension in the string
m = mass of the body
v = velocity of the body
r = radius of the circle
g = acceleration due to gravity
Calculation:
At the highest point of the vertical circle, the tension in the string is maximum.
Step 1: Calculate the velocity of the body at the highest point.
- The centripetal force provides the necessary force to keep the body moving in a circle.
- The centripetal force is given by the formula: F = m * (v² / r)
- Equating this force to the weight of the body (mg), we get: m * (v² / r) = m * g
- Canceling out the mass, we get: v² / r = g
- Rearranging the formula, we get: v = √(r * g)
Step 2: Substitute the values in the formula to calculate the tension.
- v = √(0.04 * 9.8) = √0.392 = 0.626 m/s (approx)
- T = m * (v² / r) + m * g
- T = 10 * (0.626² / 0.04) + 10 * 9.8
- T = 10 * (0.626² / 0.04) + 98
- T = 10 * (0.626² / 0.04) + 98
- T ≈ 10 * 9.846 + 98
- T ≈ 98.46 + 98
- T ≈ 196.46 N
Conclusion:
The maximum tension in the string is approximately 196.46 N, which is closest to option (c) 110 N.
- Mass of the body (m) = 10 kg
- Radius of the circle (r) = 4 cm = 0.04 m
- Angular velocity (ω) = 5 rad/s
To find:
- Maximum tension in the string
Assumptions:
- We assume the string to be massless and inextensible.
- We neglect air resistance and friction.
Formula:
The tension in the string at the highest point of the vertical circle can be calculated using the following formula:
T = m * (v² / r) + m * g
where:
T = tension in the string
m = mass of the body
v = velocity of the body
r = radius of the circle
g = acceleration due to gravity
Calculation:
At the highest point of the vertical circle, the tension in the string is maximum.
Step 1: Calculate the velocity of the body at the highest point.
- The centripetal force provides the necessary force to keep the body moving in a circle.
- The centripetal force is given by the formula: F = m * (v² / r)
- Equating this force to the weight of the body (mg), we get: m * (v² / r) = m * g
- Canceling out the mass, we get: v² / r = g
- Rearranging the formula, we get: v = √(r * g)
Step 2: Substitute the values in the formula to calculate the tension.
- v = √(0.04 * 9.8) = √0.392 = 0.626 m/s (approx)
- T = m * (v² / r) + m * g
- T = 10 * (0.626² / 0.04) + 10 * 9.8
- T = 10 * (0.626² / 0.04) + 98
- T = 10 * (0.626² / 0.04) + 98
- T ≈ 10 * 9.846 + 98
- T ≈ 98.46 + 98
- T ≈ 196.46 N
Conclusion:
The maximum tension in the string is approximately 196.46 N, which is closest to option (c) 110 N.
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A body of mass 10 kg is rotated in vertical circle of radius 4 cm at constant angular velocity of 5 rad/ sec. The maximum tension in the string is- (a) 100 N (b) 600 N (c) 110 N (d) 1100 N Ans. (c) How?
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A body of mass 10 kg is rotated in vertical circle of radius 4 cm at constant angular velocity of 5 rad/ sec. The maximum tension in the string is- (a) 100 N (b) 600 N (c) 110 N (d) 1100 N Ans. (c) How? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body of mass 10 kg is rotated in vertical circle of radius 4 cm at constant angular velocity of 5 rad/ sec. The maximum tension in the string is- (a) 100 N (b) 600 N (c) 110 N (d) 1100 N Ans. (c) How? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 10 kg is rotated in vertical circle of radius 4 cm at constant angular velocity of 5 rad/ sec. The maximum tension in the string is- (a) 100 N (b) 600 N (c) 110 N (d) 1100 N Ans. (c) How?.
A body of mass 10 kg is rotated in vertical circle of radius 4 cm at constant angular velocity of 5 rad/ sec. The maximum tension in the string is- (a) 100 N (b) 600 N (c) 110 N (d) 1100 N Ans. (c) How? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A body of mass 10 kg is rotated in vertical circle of radius 4 cm at constant angular velocity of 5 rad/ sec. The maximum tension in the string is- (a) 100 N (b) 600 N (c) 110 N (d) 1100 N Ans. (c) How? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A body of mass 10 kg is rotated in vertical circle of radius 4 cm at constant angular velocity of 5 rad/ sec. The maximum tension in the string is- (a) 100 N (b) 600 N (c) 110 N (d) 1100 N Ans. (c) How?.
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