Question

Work- energy theorem in an integral form of

• A. Newton's first law
• B. Law of equipartition of energy
• C. Newton's second law
• D. Newton's law of gravitation
• E. Newton's third law

Answer 1

The Correct Option is C

The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. This theorem is an integral form of Newton’s second law, which relates the force acting on an object to its acceleration. By integrating the force over a distance, we obtain the work done, which is equal to the change in kinetic energy. Therefore, the work-energy theorem is derived from Newton's second law.

The correct option is (C) : Newton's second law

Answer 2

The work-energy theorem states that the net work done by all the forces on a particle is equal to the change in its kinetic energy: 

\[ W = \Delta K = \frac{1}{2}mv^2 - \frac{1}{2}mu^2 \]  
This result is derived from Newton's second law: 

\[ \vec{F} = m\vec{a} \Rightarrow \vec{F} = m \frac{d\vec{v}}{dt} \Rightarrow \vec{F} \cdot d\vec{r} = m \frac{d\vec{v}}{dt} \cdot d\vec{r} \] 
Using \( \vec{v} = \frac{d\vec{r}}{dt} \), this leads to: 
\[ \vec{F} \cdot d\vec{r} = m \vec{v} \cdot d\vec{v} \Rightarrow dW = d\left( \frac{1}{2}mv^2 \right) \] 
Thus, the work-energy theorem is an integral form of Newton's second law. 

Answer: Newton's second law