Question

Given below are two statements
Statement I: If net work done is positive, the kinetic energy of a moving object increases.
Statement II: If net work done is negative, the displacement of a moving object accelerates.
In light of the above statements, choose the most appropriate answer from the options given below

• A. Statement I and II are both correct
• B. Statement I and II are both incorrect
• C. Statement I is correct but statement II is incorrect
• D. Statement II is correct but statement I is incorrect

Hint:

Positive work transfers energy to the object (increasing its speed).
Negative work (such as friction) extracts energy from the object (decreasing its speed/decelerating it).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The Work-Energy Theorem states that the net work done by all forces acting on an object is equal to the change in its kinetic energy.
This is expressed mathematically as:
\[ W_{\text{net}} = \Delta KE = KE_f - KE_i \]

Step 2: Detailed Explanation:
Let us analyze both statements based on the Work-Energy Theorem:
- Statement I: If the net work done (\(W_{\text{net}}\)) on an object is positive (\(W_{\text{net}} > 0\)):
The change in kinetic energy is positive (\(\Delta KE > 0\)), meaning:
\[ KE_f > KE_i \]
The kinetic energy of the object increases, which means the object speeds up.
Therefore, Statement I is correct.
- Statement II: If the net work done (\(W_{\text{net}}\)) is negative (\(W_{\text{net}} < 0\)):
The change in kinetic energy is negative (\(\Delta KE < 0\)), meaning:
\[ KE_f < KE_i \]
The kinetic energy of the object decreases, meaning the object slows down (decelerates).
Therefore, Statement II is incorrect because a negative net work done decelerates the object, rather than accelerating it.
Thus, Statement I is correct, but Statement II is incorrect.

Step 3: Final Answer:
Statement I is correct but Statement II is incorrect.