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NEET PHYSICSLAWS OF MOTIONMedium

Question

A body of mass 0.4 kg is whirled in a vertical circle making 2 rev/sec. If the radius of the circle is 2 m, then tension in the string when the body is at the top of the circle is:

A

41.56 N

B

89.86 N

C

109.86 N

D

122.4 N

Step-by-Step Solution

  1. Identify Given Values:
  • Mass (mm) = 0.4 kg
  • Frequency (ff) = 2 rev/sec
  • Radius (rr) = 2 m
  • Acceleration due to gravity (gg) 9.8 m/s2\approx 9.8 \text{ m/s}^2
  1. Calculate Angular Velocity (ω\omega): ω=2πf=2π(2)=4π rad/s\omega = 2\pi f = 2\pi(2) = 4\pi \text{ rad/s} [Source 43]

  2. Forces at the Top: At the highest point of a vertical circle, both the Tension (TT) and the Weight (mgmg) act downwards towards the center. The sum of these forces provides the necessary centripetal force (FcF_c). T+mg=Fc=mω2rT + mg = F_c = m\omega^2 r [Source 76, 82]

  3. Calculate Centripetal Force: Fc=0.4×(4π)2×2F_c = 0.4 \times (4\pi)^2 \times 2 Fc=0.8×16π2=12.8π2F_c = 0.8 \times 16\pi^2 = 12.8\pi^2 Using π29.87\pi^2 \approx 9.87: Fc12.8×9.87126.34 NF_c \approx 12.8 \times 9.87 \approx 126.34 \text{ N}

  4. Calculate Tension: Rearranging the force equation for TT: T=mω2rmgT = m\omega^2 r - mg T=126.34(0.4×9.8)T = 126.34 - (0.4 \times 9.8) T=126.343.92T = 126.34 - 3.92 T=122.42 NT = 122.42 \text{ N} This matches Option 4.

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 MOTIONwhirledverticalcirclemakingrevsec

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