STATEMENT-1: If a car and truck hacve same momentum then the tr5uck has more kinetic energy
STATEMENT-2: If a car and truck have same kinetic energy then the truck has more momentum.
STATEMENT-3: If a car and truck have same kinetic energy then both have same momentum

Options

A. T T F
B. F F T
C. F T F
D. T F T

Answer

To analyze the statements regarding the car and truck, we will use the relationships between momentum and kinetic energy.

### Step 1: Understanding Momentum and Kinetic Energy
- The momentum (p) of an object is given by the formula:
\[ p = mv \]
where \( m \) is the mass and \( v \) is the velocity of the object.

- The kinetic energy (K.E.) of an object is given by the formula:
\[ K.E. = \frac{1}{2} mv^2 \]

### Step 2: Analyzing Statement 1
**Statement 1:** If a car and truck have the same momentum, then the truck has more kinetic energy.

- Given that both vehicles have the same momentum, we can express this as:
\[ p_{car} = p_{truck} \implies m_{car}v_{car} = m_{truck}v_{truck} \]

- Kinetic energy is inversely proportional to mass when momentum is constant. Since the truck has a greater mass than the car, it must have a lower velocity to maintain the same momentum.

- Therefore, the kinetic energy of the truck will be less than that of the car, making this statement **false**.

### Step 3: Analyzing Statement 2
**Statement 2:** If a car and truck have the same kinetic energy, then the truck has more momentum.

- If both vehicles have the same kinetic energy, we have:
\[ K.E._{car} = K.E._{truck} \implies \frac{1}{2} m_{car} v_{car}^2 = \frac{1}{2} m_{truck} v_{truck}^2 \]

- Rearranging gives us:
\[ m_{car} v_{car}^2 = m_{truck} v_{truck}^2 \]

- Since the truck has a greater mass, it must have a greater momentum to maintain the same kinetic energy. Thus, the momentum of the truck will be greater than that of the car, making this statement **true**.

### Step 4: Analyzing Statement 3
**Statement 3:** If a car and truck have the same kinetic energy, then both have the same momentum.

- From the previous analysis, we established that if the kinetic energies are the same, the momentum of the truck (which has a larger mass) will be greater than that of the car.

- Therefore, this statement is also **false**.

### Final Conclusion
- Statement 1: False
- Statement 2: True
- Statement 3: False

### Summary of Results
- The correct answers are: False, True, False.