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NEET PHYSICSLAWS OF MOTIONEasy

Question

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

Step-by-Step Solution

  1. Identify the Force: For a body moving in a horizontal circle attached to a string, the centripetal force required to maintain the circular path is provided by the tension (TT) in the string [Source 62, 68].
  2. Formula: The centripetal force is given by Fc=mv2rF_c = \frac{mv^2}{r}. Thus, T=mv2rT = \frac{mv^2}{r}.
  3. Condition for Breaking: The string breaks if the tension exceeds the maximum tension (TmaxT_{max}). To find the maximum speed (vmaxv_{max}), we equate the tension to the breaking limit. Tmax=mvmax2rT_{max} = \frac{m v_{max}^2}{r}
  4. Calculation:
  • Mass (mm) = 0.25 kg
  • Radius (rr) = Length of string = 1.96 m
  • Max Tension (TmaxT_{max}) = 25 N 25=0.25×vmax21.9625 = \frac{0.25 \times v_{max}^2}{1.96} vmax2=25×1.960.25=100×1.96=196v_{max}^2 = \frac{25 \times 1.96}{0.25} = 100 \times 1.96 = 196 vmax=196=14 m/sv_{max} = \sqrt{196} = 14 \text{ m/s}

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from LAWS OF MOTION. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSLAWS OF MOTIONattachedstringlengthmovinghorizontal

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