For a body of given mass graph between velocity of the body and its linear momentum is

Options

A. a straight line with slope =0
B. a straight line with positive slope
C. a straight line with negative slope
D. a parabola

Answer

To solve the problem of determining the graph between the velocity of a body and its linear momentum for a given mass, we can follow these steps:

### Step 1: Understand the relationship between momentum and velocity
The linear momentum \( P \) of a body is defined as:
\[ P = m \cdot v \]
where \( m \) is the mass of the body and \( v \) is its velocity.

### Step 2: Rearranging the equation
Since the mass \( m \) is constant for a given body, we can express the relationship as:
\[ P = m \cdot v \]
This indicates that momentum \( P \) is directly proportional to velocity \( v \).

### Step 3: Identify the graph characteristics
From the equation \( P = m \cdot v \):
- If we plot momentum \( P \) on the y-axis and velocity \( v \) on the x-axis, we can see that the graph will be a straight line.
- The slope of this line will be equal to the mass \( m \), which is a constant.

### Step 4: Determine the intercept
Since both momentum and velocity are zero when the body is at rest, the graph will pass through the origin (0,0).

### Step 5: Conclusion about the graph
Thus, the graph between velocity and linear momentum for a body of given mass is a straight line that passes through the origin with a positive slope.

### Final Answer
The correct option for the graph between velocity and linear momentum for a body of given mass is a straight line with a positive slope.

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