A block of weight 4 kg is resting on a smooth horizontal plane. If it is struck by a jet of water at the rate of 2 kg `s^(-1)` and at the speed of 10 m s', then the initial acceleration of the block is

Options

A. `15 ms^(-2)`
B. `10 ms^(-2)`
C. `2.5 ms^(-2)`
D. `5 ms^(-2)`

Explanation

To solve the problem, we need to determine the initial acceleration of a block that is being struck by a jet of water. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the given data
- Weight of the block (W) = 4 kg
- Mass of the block (m) = 4 kg (since weight = mass × gravity, and we can use mass directly for calculations)
- Rate of water flow (ṁ) = 2 kg/s
- Speed of water (u) = 10 m/s

### Step 2: Calculate the force exerted by the water jet
The force exerted by the water jet can be calculated using the principle of conservation of momentum. The force (F) can be determined from the change in momentum per unit time (which is the rate of change of momentum).

The change in momentum per second (force) can be calculated as:
\[ F = \text{Rate of mass flow} \times \text{Velocity of water} \]
\[ F = ṁ \times u \]
Substituting the values:
\[ F = 2 \, \text{kg/s} \times 10 \, \text{m/s} = 20 \, \text{N} \]

### Step 3: Determine the acceleration of the block
According to Newton's second law, the acceleration (a) of the block can be calculated using the formula:
\[ F = m \times a \]
Rearranging this gives:
\[ a = \frac{F}{m} \]
Substituting the values we have:
\[ a = \frac{20 \, \text{N}}{4 \, \text{kg}} = 5 \, \text{m/s}^2 \]

### Conclusion
The initial acceleration of the block is \( 5 \, \text{m/s}^2 \).

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