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STATEMENT-1: A bus and a car having the ...

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.

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

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both statements and determine their validity based on the principles of physics, particularly kinematics and dynamics. ### Step-by-Step Solution: 1. **Understanding Statement 1**: - The statement claims that a bus and a car, both having the same kinetic energy, can come to a stop simultaneously when brakes are applied. - Kinetic energy (KE) is given by the formula: \[ KE = \frac{1}{2}mv^2 \] - If both vehicles have the same kinetic energy, it implies that the product of mass and the square of velocity for both vehicles is equal. 2. **Analyzing the Stopping Process**: - When brakes are applied, both vehicles experience deceleration (retardation) due to friction. - The stopping distance and time depend on the initial velocity and the retardation experienced by each vehicle. 3. **Understanding Statement 2**: - The second statement claims that the retardation for both the bus and the car must be the same. - Retardation (deceleration) is influenced by factors such as the mass of the vehicle, the coefficient of friction between the tires and the road, and the braking force applied. 4. **Evaluating Retardation**: - The retardation can be calculated using Newton's second law: \[ F = ma \] - Here, \(F\) is the net force (which is the friction force in this case), \(m\) is the mass of the vehicle, and \(a\) is the retardation. - Since the bus and car have different masses, the frictional force (which depends on the weight of the vehicle) will also differ, leading to different retardations unless other factors are equalized. 5. **Conclusion**: - Statement 1 is true because both vehicles can indeed stop in a dead heat if the conditions allow (sufficient friction, etc.). - Statement 2 is false because the retardation does not have to be the same for both vehicles; it depends on their respective masses and the forces acting on them. ### Final Answer: - **Statement 1**: True - **Statement 2**: False
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