Newton's second law gives the measure of

Options

A. acceleration
B. force
C. momentum
D. angular momentum

Answer

To solve the question regarding what Newton's second law measures, we can break it down step by step:

### Step 1: Understand Newton's Second Law
Newton's second law states that the force acting on an object is equal to the rate of change of its momentum. Mathematically, this can be expressed as:
\[ F = \frac{dp}{dt} \]
where \( F \) is the force, \( p \) is the momentum, and \( t \) is time.

### Step 2: Relate Momentum to Mass and Velocity
Momentum (\( p \)) is defined as the product of mass (\( m \)) and velocity (\( v \)):
\[ p = mv \]
Thus, the rate of change of momentum can be expressed as:
\[ \frac{dp}{dt} = \frac{d(mv)}{dt} \]

### Step 3: Apply the Product Rule
Using the product rule of differentiation, we can expand this:
\[ \frac{dp}{dt} = m \frac{dv}{dt} + v \frac{dm}{dt} \]
In most cases, mass (\( m \)) is constant, so:
\[ \frac{dp}{dt} = m \frac{dv}{dt} \]
Here, \( \frac{dv}{dt} \) is the acceleration (\( a \)) of the object.

### Step 4: Substitute Acceleration into the Equation
Substituting acceleration into the equation gives us:
\[ \frac{dp}{dt} = ma \]
This leads us to the conclusion that:
\[ F = ma \]
This equation shows that force is directly proportional to the mass of the object and its acceleration.

### Step 5: Conclusion
From the above steps, we can conclude that Newton's second law provides a measure of force. Therefore, the correct answer to the question is:
**B. Force**

---