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A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved
- a)14 m/s
- b)3 m/s
- c)3.92 m/s
- d)5 m/s
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A ball of mass 0.25 kg attached to the end of a string of length 1.96 ...
Given,Length of String, l = 1.96 mMass of Ball, m
= 0.25 KgMaximum Tension of String, Tmax = 25 NLet the speed of the ball is v m/sIn the horizontal circular motion of the ball tension in the string is balanced by the centrifugal force (mv2/l) and hence the maximum tension in the string will be for the maximum speed of the ball (since m and l are fixed).Therefore,Tmax=mv^2/l=> v^2=Tmax * l/m = 25 x 1.96/0.25=> v = 5 x 1.4/0.5 = 14 m/sTherefore, maximum speed of the ball will be 14 m/s.
Most Upvoted Answer
A ball of mass 0.25 kg attached to the end of a string of length 1.96 ...
Introduction
To determine the maximum speed of the ball moving in a horizontal circle without breaking the string, we analyze the forces acting on the ball.
Key Parameters
- Mass of the ball (m) = 0.25 kg
- Length of the string (radius, r) = 1.96 m
- Maximum tension (T) = 25 N
Centripetal Force Requirement
In circular motion, the tension in the string provides the necessary centripetal force to keep the ball moving in a circle. The formula for centripetal force (Fc) is:
Fc = (m * v^2) / r
Where:
- v = speed of the ball
Setting Up the Equation
Since the tension in the string is the only source of centripetal force, we set T equal to Fc:
T = (m * v^2) / r
Substituting the values:
25 N = (0.25 kg * v^2) / 1.96 m
Rearranging the Equation
Now, we solve for v^2:
v^2 = (25 N * 1.96 m) / 0.25 kg
Calculating the right side:
v^2 = (49 N*m) / 0.25 kg
v^2 = 196
Calculating Maximum Speed
Taking the square root to find v:
v = √196
v = 14 m/s
Conclusion
Thus, the maximum speed at which the ball can move without breaking the string is 14 m/s, confirming that option 'A' is correct.
To determine the maximum speed of the ball moving in a horizontal circle without breaking the string, we analyze the forces acting on the ball.
Key Parameters
- Mass of the ball (m) = 0.25 kg
- Length of the string (radius, r) = 1.96 m
- Maximum tension (T) = 25 N
Centripetal Force Requirement
In circular motion, the tension in the string provides the necessary centripetal force to keep the ball moving in a circle. The formula for centripetal force (Fc) is:
Fc = (m * v^2) / r
Where:
- v = speed of the ball
Setting Up the Equation
Since the tension in the string is the only source of centripetal force, we set T equal to Fc:
T = (m * v^2) / r
Substituting the values:
25 N = (0.25 kg * v^2) / 1.96 m
Rearranging the Equation
Now, we solve for v^2:
v^2 = (25 N * 1.96 m) / 0.25 kg
Calculating the right side:
v^2 = (49 N*m) / 0.25 kg
v^2 = 196
Calculating Maximum Speed
Taking the square root to find v:
v = √196
v = 14 m/s
Conclusion
Thus, the maximum speed at which the ball can move without breaking the string is 14 m/s, confirming that option 'A' is correct.
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A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moveda) 14 m/s b) 3 m/s c) 3.92 m/s d) 5 m/s Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moveda) 14 m/s b) 3 m/s c) 3.92 m/s d) 5 m/s Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moveda) 14 m/s b) 3 m/s c) 3.92 m/s d) 5 m/s Correct answer is option 'A'. Can you explain this answer?.
A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moveda) 14 m/s b) 3 m/s c) 3.92 m/s d) 5 m/s Correct answer is option 'A'. Can you explain this answer? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moveda) 14 m/s b) 3 m/s c) 3.92 m/s d) 5 m/s Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moveda) 14 m/s b) 3 m/s c) 3.92 m/s d) 5 m/s Correct answer is option 'A'. Can you explain this answer?.
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