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 ms^(-1)`. Take .g. constant with a value `10 ms^(-2)`. The work done by the (i) gravitational force and the (ii) resistive force of air is

Options

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`

Answer

C

Explanation

Here, `m = 1 g = 10^(-3) kg, h = 1 km = 1000m`,
`v = 50 ms^(-1), g = 10 ms^(-2)`.
(i) The work done by the gravitational force
`= mgh = 10^(3) xx 10 xx 1000 = 10 J`
(ii) The total work done by gravitational force and the resistive force of air is equal to charge in kinetic energy of rain drop.
`:. W_g + W_r = 1/2 mv^2 - 0` v
`10 + W_r = 1/2 xx 10^(-3) xx 50 xx 50 " or W_r = - 8.75 J`.