A raindrop of mass `1g` falling from a height of `1km` hits is the ground with a speed of `50 ms^(-1)`. Which of the following statements is correct? `("Taking" g= 10ms^(-2))`.

Options

A. The loss of potential energy of the drop is `10 J`
B. The gain in kinetic energy of the drop is `1.25 J`
C. The gain in kinetic energy of the drop is not equal to the loss of potential energy of the drop.
D. All of these

Answer

D

Explanation

Here , `m = 1g = 10^(-3) kg`
`h = 1 km = 1000 m`
`g = 10 ms^(-2) v = 50 ms^(-1)`
Loss of potential energy of the drop
`= mgh = (10^(3) kg) (10 ms^(-2)) (1000 m) = 10 J` (i)
Hence, option (a) is correct.
Gain in kinetic energy of the drop
`= (1)/(2) mv^(2) = (1)/(2) xx (10^(-3) kg) (50 ms^(-1))^(2) = 1.25 J` (ii)
Hence, option (b) is correct
From (i) and (ii), we get
Loss of the drop.
Hence, option ( c) is correct .