suppose the average mass of a raindrop is 3.0X10^-5 kg and their average velocity is 9 ms^-1.Calculate the energy transferredby rain to each square metre of the surface at a place which receives 100cm of rain in a year?

To determine the energy transferred by rain to each square meter of a surface receiving 100 cm of rain in a year, we need to follow a series of logical steps. This involves calculating the total mass of rain that falls on that area, the kinetic energy of the raindrops, and finally, the energy transferred per square meter.

Step 1: Calculate the Volume of Rainfall

First, we need to convert the rainfall from centimeters to meters. Since 100 cm is equal to 1 meter, we can say that 1 m³ of rain falls on each square meter of surface area in a year.

Step 2: Calculate the Mass of Rainfall

Next, we need to find the mass of the rain that falls on this area. The density of water is approximately 1000 kg/m³. Therefore, the mass of the rain that falls on 1 m² of surface area in a year can be calculated as follows:

• Mass = Volume × Density
• Mass = 1 m³ × 1000 kg/m³ = 1000 kg

Step 3: Determine the Number of Raindrops

Now, we can calculate the number of raindrops that fall on this area. Given that the average mass of a raindrop is 3.0 × 10^-5 kg, we can find the total number of raindrops:

• Number of Raindrops = Total Mass / Mass of One Raindrop
• Number of Raindrops = 1000 kg / (3.0 × 10^-5 kg) ≈ 3.33 × 10^7 raindrops

Step 4: Calculate the Kinetic Energy of Raindrops

The kinetic energy (KE) of a single raindrop can be calculated using the formula:

• KE = 0.5 × m × v²

Where:

• m = mass of one raindrop = 3.0 × 10^-5 kg
• v = velocity of raindrop = 9 m/s

Substituting the values:

• KE = 0.5 × (3.0 × 10^-5 kg) × (9 m/s)²
• KE = 0.5 × (3.0 × 10^-5 kg) × 81 m²/s²
• KE = 0.5 × 2.43 × 10^-3 kg·m²/s²
• KE ≈ 1.215 × 10^-3 J (Joules)

Step 5: Total Energy Transferred

Now, to find the total energy transferred by all the raindrops, we multiply the kinetic energy of a single raindrop by the total number of raindrops:

• Total Energy = KE × Number of Raindrops
• Total Energy = (1.215 × 10^-3 J) × (3.33 × 10^7 raindrops)
• Total Energy ≈ 4.05 × 10^4 J

Final Result

Thus, the energy transferred by rain to each square meter of the surface at a place which receives 100 cm of rain in a year is approximately 40,500 Joules.