A jet of water hits a flat stationary plate perpendicular to its motion. The jet ejects `500g` of water per second with a speed of `1m//s`. Assuming that after striking, the water flows parallel to the plate, then the force exerted on the plate is a) 5 N b) 1.0 N c) 0.5 N d) 10 N

Options

A. (a) `5N`
B. (b) `1.0N`
C. (c) `0.5N`
D. (d) `10N`

Explanation

To solve the problem, we need to calculate the force exerted on the plate by the jet of water. Here’s a step-by-step solution:

### Step 1: Understand the given data
- The mass of water ejected per second (mass flow rate) = 500 g/s = 0.5 kg/s (since 1 kg = 1000 g).
- The speed of the water jet before hitting the plate (initial speed, \( v_i \)) = 1 m/s.
- The speed of the water after hitting the plate (final speed, \( v_f \)) = 0 m/s (since the water comes to rest relative to the plate).

### Step 2: Calculate the change in momentum
The momentum \( p \) is given by the formula:
\[ p = mv \]
where \( m \) is mass and \( v \) is velocity.

The change in momentum (\( \Delta p \)) can be calculated as:
\[ \Delta p = m v_f - m v_i \]
Substituting the values:
\[ \Delta p = 0.5 \, \text{kg} \times 0 \, \text{m/s} - 0.5 \, \text{kg} \times 1 \, \text{m/s} \]
\[ \Delta p = 0 - 0.5 = -0.5 \, \text{kg m/s} \]

### Step 3: Calculate the force exerted on the plate
According to Newton's second law, the force (\( F \)) can be calculated using the formula:
\[ F = \frac{\Delta p}{\Delta t} \]
Here, \( \Delta t = 1 \, \text{s} \) (since the water is ejected at a rate of 500 g/s, which corresponds to 1 second).

Substituting the values:
\[ F = \frac{-0.5 \, \text{kg m/s}}{1 \, \text{s}} = -0.5 \, \text{N} \]
The negative sign indicates that the force is in the opposite direction of the water jet.

### Step 4: Conclusion
The magnitude of the force exerted on the plate is \( 0.5 \, \text{N} \). Since the question asks for the force exerted on the plate, we can state the answer as:
\[ \text{Force exerted on the plate} = 0.5 \, \text{N} \]

Thus, the correct answer is option (c) 0.5 N.

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