Question

Given below are two statements:
Statement I: A truck and a car moving with same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance. 
Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero. 
In the light of given statements, choose the most appropriate answer from the options given below.  

• A. Both Statement I is correct but Statement II are correct
• B. Both Statement I is correct but Statement II are incorrect
• C. Statement I is correct but Statement II is incorrect
• D. Statement I is incorrect but Statement II is correct

Answer 1

The Correct Option is C

To determine the correctness of the given statements, let's analyze each statement individually:

Statement I: "A truck and a car moving with the same kinetic energy are brought to rest by applying brakes which provide equal retarding forces. Both come to rest in equal distance."

Explanation: Kinetic energy (K.E.) is given by K.E. = \frac{1}{2}mv^2. If both vehicles have the same kinetic energy, we can set their kinetic energies equal:

\frac{1}{2}m_1v_1^2 = \frac{1}{2}m_2v_2^2

Given that the same retarding force (F) brings both vehicles to rest, the work done to stop the vehicles is the same. Since work done by the force is equal to the change in kinetic energy,

Fd = \frac{1}{2}m_1v_1^2 \quad \text{and} \quad Fd = \frac{1}{2}m_2v_2^2

Both vehicles come to rest over the same distance (d), which makes this statement correct.

Statement II: "A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero."

Explanation: When a car changes direction with constant speed, its velocity vector changes, indicating a change in velocity. Acceleration is the rate of change of velocity. When a car changes direction, even with constant speed, it is subject to centripetal acceleration, as the velocity vector's direction changes.

Hence, because the velocity changes direction, the car indeed has acceleration. Therefore, Statement II is incorrect.

Conclusion: Considering these analyses, the correct answer is: Statement I is correct but Statement II is incorrect.