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NEET PHYSICSRotational motionMedium

Question

A man of 50 kg50 \text{ kg} mass is standing in a gravity free space at a height of 10 m10 \text{ m} above the floor. He throws a stone of 0.5 kg0.5 \text{ kg} mass downwards with a speed 2 m s−12 \text{ m s}^{-1}. When the stone reaches the floor, the distance of the man above the floor will be:

A

9.9 m9.9 \text{ m}

B

10.1 m10.1 \text{ m}

C

10 m10 \text{ m}

D

20 m20 \text{ m}

Step-by-Step Solution

In a gravity-free space, there is no external force acting on the system consisting of the man and the stone. Therefore, the total momentum of the system is conserved. Initial momentum of the system = 00 (since both are at rest). Let the velocity of the stone be vsv_s and the velocity of the man be vmv_m. Taking the upward direction as positive, vs=−2 m s−1v_s = -2 \text{ m s}^{-1}. According to the law of conservation of momentum: mmvm+msvs=0m_m v_m + m_s v_s = 0 50×vm+0.5×(−2)=050 \times v_m + 0.5 \times (-2) = 0 50vm−1=050 v_m - 1 = 0 vm=150=0.02 m s−1v_m = \frac{1}{50} = 0.02 \text{ m s}^{-1} So, the man moves upwards with a constant speed of 0.02 m s−10.02 \text{ m s}^{-1}. The time taken by the stone to reach the floor (a distance of 10 m10 \text{ m} downwards) is: t=DistanceSpeed=10 m2 m s−1=5 st = \frac{\text{Distance}}{\text{Speed}} = \frac{10 \text{ m}}{2 \text{ m s}^{-1}} = 5 \text{ s} In this time of 5 s5 \text{ s}, the upward distance moved by the man is: dm=vm×t=0.02 m s−1×5 s=0.1 md_m = v_m \times t = 0.02 \text{ m s}^{-1} \times 5 \text{ s} = 0.1 \text{ m} The final distance of the man above the floor is his initial height plus the distance moved upwards: Final height = 10 m+0.1 m=10.1 m10 \text{ m} + 0.1 \text{ m} = 10.1 \text{ m}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Rotational 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.

PHYSICSRotational motionstandinggravityheightthrowsdownwards

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