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Physics · WORK, ENERGY AND POWER
हिन्दीA spherical raindrop of radius \( 2\text{ mm} \) falls from a height of \( 500\text{ m} \) above the ground. It experiences air resistance such that its speed upon reaching the ground is \( 10\text{ m s}^{-1} \). Taking \( g = 10\text{ m s}^{-2} \) and the density of water as \( 10^3\text{ kg m}^{-3} \), the work done by the resistive force during the entire descent is:
Correct answer · Option 2
\( -0.166\text{ J} \)
Explanation
Mass \( m = \frac{4}{3}\pi r^3 \rho = \frac{4}{3}\pi (2\times 10^{-3})^3 (10^3) = 3.35 \times 10^{-5}\text{ kg} \). \( W_g = mgh = 3.35 \times 10^{-5} \times 10 \times 500 = 0.1675\text{ J} \). Change in KE \( \Delta K = \frac{1}{2}mv^2 = 0.5 \times 3.35\times 10^{-5} \times 100 = 0.001675\text{ J} \). By work-energy theorem, \( W_{\text{res}} = \Delta K - W_g = 0.001675 - 0.1675 \approx -0.166\text{ J} \).
