Question

The velocity-mass graph of a body with constant linear momentum is represented by the graph:

• A. Hyperbolic decreasing curve
• B. Straight line decreasing
• C. Curved decreasing (non-hyperbolic)
• D. Straight line increasing

Hint:

If a product of two variables is constant (like \(mv = \text{constant}\)), their graph is a rectangular hyperbola.

Answer 1

The Correct Option is A

Step 1: Write expression for linear momentum.
\[ p = mv \]

Step 2: Use condition of constant momentum.
If momentum is constant:
\[ mv = \text{constant} \]

Step 3: Express velocity in terms of mass.
\[ v = \frac{p}{m} \]

Step 4: Analyze the relation.
Velocity is inversely proportional to mass:
\[ v \propto \frac{1}{m} \]

Step 5: Identify graph nature.
An inverse relation between two variables gives a rectangular hyperbola.

Step 6: Interpret physically.
As mass increases, velocity decreases such that their product remains constant.

Step 7: Final answer.
\[ \boxed{\text{Hyperbolic decreasing curve}} \]