It is well known that a rain drop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop, but is otherwise undetermined. Consider a drop of mass 1.0g falling from a height of 1.00km. It hits the ground with a speed of `50.0ms^(-1)` (a) What is the work done by the gravitational force ? (b) What is the work done by the unknown resistive force ?

Options

A. `(i) -10J` `(ii) -8.25J`
B. `(i) 1.25J` `(ii)-8.25 J`
C. `(i)100J` `(ii) 8.75 J`
D. `(i) 10J` `(ii) -8.75 J`

Answer

D

Explanation

Work done by gravity `=mgh=(10^(-3))xx10xx10^(3)`
`=10J`
Work done by resistive force `=` final energy
`-` initial energy
`=(0+(1)/(2)m upsilon^(2))-(mgh+0)=(1)/(2)m upsilon^(2)-mgh`
`=(1)/(2)xx10^(-3)xx50^(2)-10^(-3)xx10xx10^(3)=-8.75J`