STATEMENT-1: A bus and a car having the same kinetic energy are brought to rest by the applications of brakes. Assume that on application of brakes, rotational motion of wheels ceases and both may stop in dead heat.
because
STATEMENT-2: Retardation for both bus and truck must be same.

Options

A. Statement-1 is True, Statement-2 is True, Statement -2 is a correct explanation for
Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement -2 is NOT a correct explanation for
Statement-1
C. Statement 1 is True, Statement-2 is False
D. Statement - 1 is False, Statement-2 is True

Answer

To analyze the statements given in the question, we will break down the problem step by step.

### Step 1: Understanding the Statements
- **Statement 1**: A bus and a car having the same kinetic energy are brought to rest by the application of brakes. It is assumed that the rotational motion of the wheels ceases, and both may stop in a dead heat.
- **Statement 2**: Retardation for both the bus and the car must be the same.

### Step 2: Analyzing Statement 1
- Both the bus and the car have the same kinetic energy initially. Kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is mass and \( v \) is velocity.
- Since both vehicles have the same kinetic energy, we can conclude that the work done by the brakes to bring them to rest will also be equal.

### Step 3: Work-Energy Principle
- According to the work-energy principle, the work done on an object is equal to the change in its kinetic energy. Since both vehicles have the same initial kinetic energy and come to rest, the work done by the brakes on both vehicles is equal.

### Step 4: Understanding Retardation
- Retardation (deceleration) is defined as the negative acceleration experienced by an object when it is slowing down. It can be calculated using Newton's second law:
\[ F = ma \]
where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration (or retardation in this case).

### Step 5: Comparing Forces and Masses
- The force applied by the brakes is what brings the vehicles to rest. Assuming the braking force is the same for both vehicles (which is a simplification), we can express the retardation as:
\[ a = \frac{F}{m} \]
- Since the bus has a larger mass than the car, if both experience the same braking force, the retardation of the bus will be less than that of the car.

### Step 6: Conclusion
- **Statement 1** is true because both vehicles can stop in a dead heat due to equal work done.
- **Statement 2** is false because the retardation cannot be the same; it will differ due to the difference in mass.

### Final Answer
- Statement 1 is true, and Statement 2 is false.