Question

A rain drop starts falling from a height of $2km$. It falls with a continuously decreasing acceleration and attains its terminal
velocity at a height of $1km$. The ratio of the work done by the gravitational force in the first half to the that in the second
half to the drops journey is

• A. $1:1$ and the time of fall of the drop in the two halves is $a:1$ (where $a>1$)
• B. $1:1$ and the time of fall of the drop in the two halves is $a:1$ (where $a<1$)
• C. $a:1$ (where $a>1$) and the time of fall of the drop in the two halves is $1:1$
• D. $a:1$ (where $a<1$) and the time of fall of the drop in the two halves is $1:1$

Answer 1

The correct option is A $1:1$ and the time of fall of the drop in the two halves is $a:1$ (where $a>1$)

Since the height of fall is $1km$ being very small compared to the radius of the earth we can assume to remain constant throughout (The work done $mgx$ for $x$ distance moved) is clearly same for both values of the rain drops journey. Since the drop attains speed $V$ at the end of first half of journey average speed during half is $V/2$. The speed of the drop during second half is constant and equal to $V$ through out. The time of fall of the drop during the first half is therefore greater than the corresponding time during second half. So, correct answer is $1:1$ and the time of fall of the drop in the two halves is $a:1$ where $a>1$.