It is well known that a raindrop falls under the influence of the downward gravitational force and opposing resistive force. The latter is known to be proportional to the speed of the drop. Consider a drop of mass 1 gm falling from a height of 1 km. If it hits the ground with a speed of 50 ms -1 . The work done by the resistive force is

Question

It is well known that a raindrop falls under the influence of the downward gravitational force and opposing resistive force. The latter is known to be proportional to the speed of the drop. Consider a drop of mass 1 gm falling from a height of 1 km. If it hits the ground with a speed of 50 ms -1 . The work done by the resistive force is (A) -1.25 J (B) -4.75 J (C) -8.75 J (D) -10 J

Tardigrade Admin · Accepted Answer

Wr=Δ K+Δ U=(1/2) m v2-m g h =((1/2) × 10-3 × 502)-(10-3 × 10 × 103) =1.25-10=-8.75 J

-1.25 J

-4.75 J

-8.75 J

-10 J

Wr​=ΔK+ΔU=21​mv2−mgh =(21​×10−3×502)−(10−3×10×103) =1.25−10=−8.75J

$W_{r} = Δ K + Δ U = \frac{1}{2} m v^{2} - m g h$
$= (\frac{1}{2} \times 1 0^{- 3} \times 5 0^{2}) - (1 0^{- 3} \times 10 \times 1 0^{3})$
$= 1.25 - 10 = - 8.75 J$