The linear momentum of a body changes at the rate of `10kgms^(-1)` per second Force acting on the body is

Options

A. 1N
B. 10N
C. 1kg f
D. 10 kg f

Answer

To find the force acting on the body when the linear momentum changes at a rate of \(10 \, \text{kg m/s}^2\), we can use the relationship between force and momentum.

### Step-by-Step Solution:

1. **Understand the relationship between force and momentum**:
The force acting on an object is equal to the rate of change of its momentum. Mathematically, this is expressed as:
\[ F = \frac{dP}{dt} \]
where \(F\) is the force, \(P\) is the momentum, and \(t\) is time.

2. **Identify the rate of change of momentum**:
According to the problem, the linear momentum of the body changes at a rate of \(10 \, \text{kg m/s}^2\). This means:
\[ \frac{dP}{dt} = 10 \, \text{kg m/s}^2 \]

3. **Substitute the rate of change of momentum into the force equation**:
Now, substituting the value of \(\frac{dP}{dt}\) into the force equation:
\[ F = 10 \, \text{kg m/s}^2 \]

4. **Convert kg m/s² to Newtons**:
By definition, \(1 \, \text{kg m/s}^2\) is equivalent to \(1 \, \text{Newton}\). Therefore:
\[ F = 10 \, \text{N} \]

5. **Conclusion**:
The force acting on the body is \(10 \, \text{N}\).

### Final Answer:
The force acting on the body is \(10 \, \text{N}\).