A jet of water having velocity = 10m/sand stream cross-section = 2cm2hits a flat plate perpendicularly, with the water splashing out parallel to plate. The plate experiences a force of :a)20Nb)10Nc)10Nd)8NCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

The correct answer is: 20 N

Answer

Given:
- Velocity of the jet of water = 10 m/s
- Cross-section area of the stream = 2 cm²

To find:
The force experienced by the flat plate when the water hits it perpendicularly.

Solution:

Step 1: Calculate the momentum of the water stream:
Momentum = mass × velocity

The mass of the water stream can be calculated using the formula:
mass = density × volume

The density of water is approximately 1000 kg/m³.

Volume = area × length

Given that the cross-section area of the stream is 2 cm², we need to convert it to m²:
Area = 2 cm² = 2 × 10⁻⁴ m²

Assuming the length of the stream is 1 m (as it is not provided), the volume can be calculated as:
Volume = 2 × 10⁻⁴ m² × 1 m = 2 × 10⁻⁴ m³

Now, we can calculate the mass of the water stream:
mass = 1000 kg/m³ × 2 × 10⁻⁴ m³ = 0.2 kg

The momentum of the water stream can be calculated as:
momentum = mass × velocity = 0.2 kg × 10 m/s = 2 kg·m/s

Step 2: Calculate the force experienced by the flat plate:
The force experienced by an object can be calculated using the formula:
force = rate of change of momentum

In this case, the rate of change of momentum is equal to the momentum of the water stream hitting the plate per second:
force = momentum / time

Since the water is hitting the plate perpendicularly, the time taken for the water stream to hit the plate is negligible.

Therefore, the force experienced by the flat plate is:
force = 2 kg·m/s / 1 s = 2 N

Conclusion:
The flat plate experiences a force of 2 N when the jet of water hits it perpendicularly. Therefore, the correct answer is option 'A' (20 N).

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