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 volume `10 m//s^(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

Apply work energy theorem
`W_("all force")=K_t-K_1`

W=mgh
`=10^(-3)xx10xx10^3`
=10 J
`(U_1-U_2)+W_n=1/2mv^2-0` [`K_1`=0,u-0 ]
mgh+`W_n=1/2mv^2` [`U_2=0`]
`10^(-3)xx10xx1000W_n=1/2xx10^(-3)xx(50)^3`
`10+W_n=1.25`
`uarr`
Work done by gravitational force
`W_("fr")=-8.75J`