A rain drop starts falling from a height of 1 km. It falls with a continuously decreasing acceleration and attains its constant terminal speed
A rain drop starts falling from a height of 1 km. It falls with a continuously decreasing acceleration and attains its constant terminal speed after falling through a height of 500 m. Then, the work done by the gravitational force in the first half and the second half of the drop's journey are in the ratio
(a) 1 : 1 and the times of fall of the drop in the two halves are in the ratio n:1 (where n >1)
(b) 1 : 1 and the times of fall of the drop in the two halves are in the ratio n :1 (where n <1)
(c) n : 1 (where n >1) and the times of fall of the drop in the two halves are in the ratio 1 : 1
(d) n : 1 (where n < 1) and the times of fall of the drop in the two halves are in the ratio 1 : 1
1 Answers
The correct option is (a) 1 : 1 and the times of fall of the drop in the two halves are in the ratio n:1 (where n >1).
Explanation:
Since, the height of fall 1 km being very small compared to the radius of earth, we can assume g to remain constant throughout. The work done (mgx, for x distance moved) is clearly same for both the halves of the rain drops journey.
Since the drop starts from rest and attains a speed v at the end of the first-half of its journey, its average speed during this half is v/2. The speed of the drop during the second-half is constant and equal to v throughout. The time of fall of the drop during the first-half is therefore greater than the corresponding time during the second-half.