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A : If m and m(e) are moving mass, rest ...

A : If m and `m_(e)` are moving mass, rest mass of a body and c is velocity of light, then kinetic energy of the body is `E=(m-m_(0))c^(2)`
R : Total energy of a body is sum of kinetic energy and rest mass energy.

A

If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).

B

If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).

C

If Assertion is true statement but Reason is false, then mark (3).

D

If both Assertion and Reason are false statements, then mark (4).

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the two statements provided: **Statement A**: The formula for kinetic energy is given as \( E = (m - m_0)c^2 \), where \( m \) is the moving mass and \( m_0 \) is the rest mass of the body. **Statement R**: The total energy of a body is the sum of kinetic energy and rest mass energy. ### Step-by-Step Solution: 1. **Understanding the Terms**: - \( m \): Moving mass (also referred to as relativistic mass). - \( m_0 \): Rest mass of the body. - \( c \): Speed of light in a vacuum. 2. **Kinetic Energy in Relativity**: - In the context of special relativity, the total energy \( E \) of a body is given by the equation: \[ E = mc^2 \] - The rest mass energy is given by: \[ E_0 = m_0c^2 \] - The kinetic energy \( K \) can be derived from the total energy by subtracting the rest mass energy: \[ K = E - E_0 = mc^2 - m_0c^2 \] - This simplifies to: \[ K = (m - m_0)c^2 \] - Hence, the formula \( E = (m - m_0)c^2 \) is indeed the expression for kinetic energy. 3. **Evaluating Statement A**: - Since we derived that \( K = (m - m_0)c^2 \), Statement A is **correct**. 4. **Evaluating Statement R**: - The total energy \( E \) of the body is the sum of kinetic energy \( K \) and rest mass energy \( E_0 \): \[ E = K + E_0 \] - Substituting the expressions we have: \[ E = (m - m_0)c^2 + m_0c^2 = mc^2 \] - This confirms that Statement R is also **correct**. 5. **Conclusion**: - Both statements A and R are correct. ### Final Answer: Both statements A and R are correct.
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