Question

A raindrop of mass 1 g falling from a height of 1 km hits the ground with a speed of . Which of the following statements is correct?

(Take$g = 10 m s ^ { - 2 }$)

• 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 1

Answer: (D)

All of these

Answer 2

Here, $\mathrm { m } = 1 \mathrm {~g} = 10 ^ { - 3 } \mathrm {~kg}$

h = 1km = 1000m

g = 10 m, v = $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

Loss of potential energy of the drop

…(i)

Hence, option (1) is correct.

Gain in kinetic energy of the drop

$= \frac { 1 } { 2 } \mathrm { mv } ^ { 2 } = \frac { 1 } { 2 } \times \left( 10 ^ { - 3 } \mathrm {~kg} \right) \left( 50 \mathrm {~ms} ^ { - 1 } \right) ^ { 2 } = 1.25 \mathrm {~J}$ …(ii)

Hence, option (2) is correct.

From (i) and (ii), we get

Loss of potential energy of the drop $\neq$ Gain in kinetic energy of the drop.

Hence, option (3) is also correct.