Question

A rain drop of mass m is falling vertically through the air with a steady speed v. The rain drop experiences a retarding force of kv due to the air, where is a constant. The acceleration of free fall is a Which of the following will KE of the drop

a.Mg/k
b. Mg²/2K²
C. M³g²/K²
d M³g²/2K²​

Answer 1

Answer:

option D

Explanation:

For raindrop to fall with a steady speed v, terminal speed must be reached (net force and thus, net acceleration is zero).

This occurs when the retarding force kv equals to the weight mg.

So, mg = kv giving v = mg / k.

Kinetic energy of raindrop,

$ke = \frac{1}{2} mv {}^{2}$

$= \frac{1}{2} m( \frac{mg}{k} ) {}^{2}$

$= \frac{m {}^{3} {g}^{2} }{2 {k}^{2} }$

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