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NEET PHYSICSMOTION IN A STRAIGHT LINEMedium

Question

A balloon is at a height of 81 m81 \text{ m} and is ascending upwards with a velocity of 12 m/s12 \text{ m/s}. A body of 2 kg2 \text{ kg} weight is dropped from it. If g=10 m/s2g=10 \text{ m/s}^2, the body will reach the surface of the earth in:

A

1.5 s

B

4.025 s

C

5.4 s

D

6.75 s

Step-by-Step Solution

  1. Identify Initial Conditions: When an object is dropped from a moving body (like a balloon), it acquires the initial velocity of that body at the instant of release.
  • Initial velocity (uu) = +12 m/s+12 \text{ m/s} (directed upwards).
  • Displacement (ss) = −81 m-81 \text{ m} (taking upward direction as positive, the final position (ground) is 81 m81 \text{ m} below the point of release).
  • Acceleration (aa) = −g=−10 m/s2-g = -10 \text{ m/s}^2 (acting vertically downwards).
  • The mass of the body (2 kg2 \text{ kg}) does not affect the kinematics of free fall (neglecting air resistance) .
  1. Apply Equation of Motion: Use the displacement-time relation: s=ut+12at2s = ut + \frac{1}{2}at^2 . −81=12t+12(−10)t2-81 = 12t + \frac{1}{2}(-10)t^2 −81=12t−5t2-81 = 12t - 5t^2
  2. Solve the Quadratic Equation: Rearrange the terms to form 5t2−12t−81=05t^2 - 12t - 81 = 0. Using the quadratic formula: t=−b±b2−4ac2at = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} t=12±(−12)2−4(5)(−81)2(5)t = \frac{12 \pm \sqrt{(-12)^2 - 4(5)(-81)}}{2(5)} t=12±144+162010=12±176410t = \frac{12 \pm \sqrt{144 + 1620}}{10} = \frac{12 \pm \sqrt{1764}}{10} t=12±4210t = \frac{12 \pm 42}{10} Possible values: t1=5.4 st_1 = 5.4 \text{ s} and t2=−3 st_2 = -3 \text{ s}. Since time cannot be negative, t=5.4 st = 5.4 \text{ s}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOTION IN A STRAIGHT LINE. 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.

PHYSICSMOTION IN A STRAIGHT LINEballoonheightascendingupwardsvelocity

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