Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value 10 m/s2. The work done by the (i) gravitational force and the (ii) resistive force of air is :-

Question

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take 'g' constant with a value 10 m/s2. The work done by the (i) gravitational force and the (ii) resistive force of air is :- (A) (i) 1.25 J (ii) - 8.25 J (B) (i) 100 J (ii) 8.75 J (C) (i) 10 J (ii) - 8.75 J (D) (i) - 10 J (ii) - 8.25 J

Tardigrade Admin · Accepted Answer

Sol. wg+wa=Kf-Ki m g h+ wa=(1/2) m v2-0 10-3 × 10 × 103+wa=(1/2) × 10-3 ×(50)2 wa=-8.75 J i.e. work done due to air resistance and work done due to gravity =10 J

Q. Consider a drop of rain water having mass $1 g$ falling from a height of $1 km$ . It hits the ground with a speed of $50 m / s$ . Take 'g' constant with a value $10 m / s^{2}$ .
The work done by the
(i) gravitational force and the
(ii) resistive force of air is :-

(i) 1.25 J (ii) - 8.25 J

(i) 100 J (ii) 8.75 J

(i) 10 J (ii) - 8.75 J

(i) - 10 J (ii) - 8.25 J

Sol. $w_{g} + w_{a} = K_{f} - K_{i}$
$m g h + w_{a} = \frac{1}{2} m v^{2} - 0$
$1 0^{- 3} \times 10 \times 1 0^{3} + w_{a} = \frac{1}{2} \times 1 0^{- 3} \times (50)^{2}$
$w_{a} = - 8.75 J$ i.e. work done due to air resistance and work done due to gravity $= 10 J$

Q. Consider a drop of rain water having mass 1g falling from a height of 1km. It hits the ground with a speed of 50m/s. Take 'g' constant with a value 10m/s2. The work done by the (i) gravitational force and the (ii) resistive force of air is :-