Statement-1: Kinetic energy of system = \( \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2 + \dots + \frac{1}{2} m_n v_n^2 \)
Statement-2: Kinetic energy of system = Kinetic energy of center of mass + kinetic energy with respect to center of mass.
Show Hint
- Statement I is true; Statement II is true
- Statement I is true; Statement II is false
- Statement I is false; Statement II is true
- Statement I is false; Statement II is false
The Correct Option is A
Solution and Explanation
Step 1: Analyze Statement 1.
The total kinetic energy of a system of particles is the sum of the kinetic energies of each particle. This matches Statement 1: \[ KE_{\text{total}} = \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2 + \dots + \frac{1}{2} m_n v_n^2. \] Thus, Statement 1 is true.
Step 2: Analyze Statement 2.
The kinetic energy of a system can also be described as the kinetic energy of the center of mass (which is \( \frac{1}{2} M V_{\text{cm}}^2 \)) plus the kinetic energy due to the motion of particles relative to the center of mass. This matches Statement 2.
Step 3: Conclusion.
Both Statement 1 and Statement 2 are correct.
Final Answer: \[ \boxed{\text{Statement I is true; Statement II is true.}} \]
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