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